Restricted Free Agent Question

Does a player have to take the higher offer from a team if they offer him more money?
If a player gets offered 10 million from another team, and 9 million from his old team, does he have to go to the team where he gets offered 10 mil? Or does his old team have to match that 10 mil or more? Same with unrestricted FAs, if a player gets offered less from one team, can he still go to that team?

Restricted FAs are sign to offer sheets first. It's up to the team wherein they're at if they're gonna match or not.

For example: Elton Brand was signed to an $14M offer sheet by the Heat. The Clippers do have a choice to match the $14M offered by Miami.

Are players' old teams allowed to offer more than nay other team's max offer too? For example, that's how the Lakers were able to give Kobe a larger contract than teams who had CAP like the Clippers.

Does a player have to take the higher offer from a team if they offer him more money?
If a player gets offered 10 million from another team, and 9 million from his old team, does he have to go to the team where he gets offered 10 mil? Or does his old team have to match that 10 mil or more? Same with unrestricted FAs, if a player gets offered less from one team, can he still go to that team?

The player's only limitation is he must sign w/ his old team if they match the offer or exceed it. He can refuse higher offers from new teams.

The old team can always offer more money than any new teams, if the team wishes to.

Are players' old teams allowed to offer more than nay other team's max offer too? For example, that's how the Lakers were able to give Kobe a larger contract than teams who had CAP like the Clippers.

I'm not sure if they're able to or not, but there's really no reason for them to do so when they can simply match the offer sheet and retain the player.

So if they match the offer sheet, the player doesnt have a choice of team?

That's correct. Furthermore, he cannot be traded to the team he signed an offer sheet with for one season.

Will the new CBA change anything regarding restricted/ unrestricted FAs? Also, since restricted free agency allows the old team to decide whether or not to keep a player, which obviously is an advantage, what's the incentive for teams to sign players to an unrestricted contract?

I don't think restricted free agency was eliminated in the new CBA but I could be wrong. I believe restricted free agency was introduced to prevent up and coming players bolting once the contract they signed as a rookie expired. If I recall correctly, it's not something teams choose to do with individual players.

The only thing about free agency that changes in the CBA is that the max length of a contract is changed. I think for old teams it went down from 7 to 6 years, for new teams from 6 to 5 years or something like that. There is of course the hgher salary cap and roster extension to 14 players, which will effect how many and how much players get paid.

Andrew's right, you usually only see restricted free agents at the end of rookie contracts. For 2nd and later contracts, it's usually a straightforward Player Option or Team Option.