This is my compilation of free agency and arbitration rules. I will add on to this as I discover more information:
Arbitration
A player may not make less than the league minimum of $200,000.
Players with one or two years of service time and players between two and three years of service time (except for the 17% with the most service time) can have their contracts renewed automatically by the team if they cannot come to an agreement. When renewing a contract, a team cannot reduce a player's pay by more than 20% from the prior year or 30% from the year before that.
Players with 3, 4, or 5 years of service time and the top 17% of the 2 year players may opt for arbitration in order to come to a contract.
The club' proposal may not be less than 80% of the player's salary the previous year. The exception here is that if a player won an arbitration award the prior year that resulted in a 50% or greater salary increase, there is no maximum paycut allowed in the proposal.
Arguments that are not allowed in an arbitration hearing include the state of the team's finances, previous offers made during salary negotiations between the player and the team, any press comments or testimonials with the exception of media-supported awards like the MVP Award or salaries in other sports or occupations.
A player with a non-guaranteed contract or an arbitration award may be released up until the 15th day of spring training with 30 days' pay or from the 16th day of spring training until the opening of the season with 45 days' pay.
When a player is claimed on waivers, the new team takes on the contract. When a player is released in the middle of a guaranteed contract, the new team only has to pay league minimum with the old team footing the rest of the bill.
Free Agency and Compensation
A player that has accrued 6 complete years or more of service time at the end of a season and does not have a contract is eligible for filing for free agency, after which the player can sign with any team he wants.
To receive compensation for a player that signs with another team, the team must offer the player salary arbitration.
The team must offer salary arbitration to the player by December 7 or will not be allowed to negotiate with or sign the player until the following May 1. After arbitration is offered, the player has until December 19 to either accept or refuse salary arbitration. If it is refused, the player can only negotiate with the club until January 7th, after which no more negotiation can take place until May 1.
The compensation formula is based off a negotiated formula, heavy on triple crown stats, for the previous 2 seasons. Type A players are those that rank in the top 30% of his position. Type B players are those that rank below top 30% but still in the top 50%. Type C players are those that rank in the top 60% but not the top 50%.
A type players fetch the 1st-round draft pick of teams in the top half of W-L record or a 2nd-round draft pick of teams in the bottom half of W-L record and an additional pick between the 1st and 2nd rounds. B types don't get the sandwich pick and C type players fetch a sandwich between the 2nd and 3rd rounds. The higher the player's ranking in the compensation formula, the higher priority the old team gets in acquiring draft picks.
Something that's never mentioned is that there are still limits to the type of free agents that teams may sign.
If there are 14 or less type A and B players available, no team may sign more than 1 type A or B player. If there are 15-38 available A and B players, no team may sign more than 2. From 39-62 this becomes 3. The club quota increases accordingly for higher totals of available free agents. There is no maximum allowed for type C free agents. Lastly, a team can sign up to as many type A and B free agents as they've lost, regardless of the above quota.
Major League free agents come with an automatic no-trade clause until after the next June 15.
Rule 5 Draft
Once a player is signed by an organization either through the draft or as a free agent, the clock immediately starts ticking on the club's exclusive rights to the player.
After 3 complete minor league seasons (or 4 if the player was younger than 19 on the preceding June 5), a player comes to one of the major crossroads of his career. At this point, a team has to decide if they want to sign the player to a major-league contract (adding him to the 40-man roster which consists of 25 active players and 15 on optional assignment) or if they want to let the other teams have a shot at him.
Players that have the minor league seasons required and are not added to the 40-man roster are eligible for baseball's Rule 5 draft. A player can be drafted by another organization for a sum of $50,000. The catch, however, is that if the player is ever removed from his new team's 25-man roster during the next season, he has to be offered back to the original club for half the price, or $25,000.
A player not on the 40-man roster and not taken in the Rule 5 draft remains under contract with his current organization. If the player has less than 6 years of minor league service, he can elect to be a minor league free agent, thus getting out of Rule 5 consideration for all intents and purposes.
Service Time
Service time is accrued for every day spent in the majors. If a player spends 20 days or less of the season on optional assignment, the player is given service time for the entire season. This is to prevent various shenanigans if calling up a player at the end of April to buy an extra year of rights.
Service time allows the player more authority over how his contract can be assigned.
A player with 10 years or more Major League service, the last 5 being with the team he's currently on may not be assigned to another team without his consent.
A player with 5 years or more Major League service cannot be optioned to the minors without his permission. He must be offered his release. In the case of a player signed to a Major League contract as a free agent, and thus almost certainly signed to a guarantee contract, still has to be paid according to the provisions of his contract.
A player with 3 years or more Major League service may not be removed from the 40-man roster without his permission. The player can opt to be released immediately or at the end of the season.
A player may elect to become a free agent whenever he is removed from the 40-man roster starting with the second removal of his career. The player may opt to not become a free agent but to become a free agent after the season.
A player with 5 years or more Major League service that is traded in the middle of a multi-year contract may, during the offseason, require his new team to either trade him or let him become a free agent. If the player is eventually traded, he's not eligible to demand a trade again under the current contract and loses free agency rights for 3 years.
The 40-Man Roster and Options
Now that the player is on the 40-man roster, another clock starts ticking. He's signed to what amounts to a major-league contract, but the organization has a limited number of seasons in which to keep the player on the team for good. A player can be removed from the 40-man roster at any time, but removing a player from the 40-man roster results in the player having to pass through waivers.
Once a player is added to the 40-man roster, the parent club can send him down to the minors on "optional assignment" in 3 separate seasons. You don't need to actually be on the 25-man roster for an option year to be used; being on the 40-man roster in spring training and optioned to the minors before the season is enough to make the season count as an option year. If a player is never sent down, however, he doesn't use an option year.
Also, despite it being a major league contract, the minimum for players on the 40-man roster and not the 25-man roster is $37,000 plus collective cost of living increases since 1999.
After the three option years are up, a player must pass through waivers to be placed on optional assignment.
When a player is designated for assignment, the player is essentially in limbo. He doesn't count against any of the roster sizes and this is used while you either try to trade the player or get him to accept a minor league assignment.
When a player is placed on waivers, other teams have a shot at claiming him, in order of worst record in the same league to best record in same league to worst record in opposing league to best team in opposing league. For the first month of the season, the W-L record of the previous season is used. When a team places a waiver claim on a player, the new team is subject to the same option rules. For example, if the Red Sox claim Joe Schmoe off waivers because he was out of options when the Devil Rays sent him down, the Red Sox would then have still to pass Schmo through waivers to send him down to their own minor league team.
There are two disabled lists in the majors. The 15-day disabled list forces teams to keep players out for a minimum of 15 days and does not count against the 25-man roster. The 60-day or Emergency disabled list requires a minimum of 60 days on the shelf and doesn't count against either the 25-man or 40-man roster.