UPDATE:
17) When do teams need to sign players by for them to be eligible to play in the playoffs? Is it true that Joe Smith, Stephon Marbury, etc., need to be signed by the Celtics prior to March 1 to be on the playoff roster?
To be eligible to play in the playoffs, a player must be *waived* no later than March 1. So long as that player is waived by such date, he can sign at any point prior to the last day of the regular season and still play in the playoffs.
18) How much money do the Celtics have to offer a free agent? Could the Cavaliers outspend us?
Boston has $2.392 of the MLE left; Cleveland has $5.135 million. The amount each team can offer Smith is reduced by 1/180 for every day after January 10, meaning that if Smith signs a contract on, say, March 1, his contract is reduced by 50/180s. In such instance, Boston could offer a maximum of $1.66 million, and Cleveland could offer a maximum of $3.71 million. It's not necessarily likely that either team will go that high, but they could if they wished to.
Additionally, each team can offer a pro-rated share of its "LLE", described above. Lastly, any team can sign a player to a minimum contract at any time, so long as they have fewer than 15 players on their roster.