You know, for someone who keeps sneering about how ignorant everyone else is, you really could stand to read Coon's CBA FAQ. Claiming to have superior knowledge and actually having it are two different things.
http://members.cox.net/lmcoon/salarycap.htm#19
Bird rights kick in after three years, generally speaking. There is no reason that a second-round pick or undrafted rookie can't be signed to a three-year deal. It's just almost never done.
Without Bird rights, a team must either have cap space or use one of their exceptions (most typically the MLE) in order to re-sign one of their free agents.
An "Early Bird" exception can be used after two years in order to re-sign the player up to 175% of his original salary. The new contract must be at least two years long.
http://members.cox.net/lmcoon/salarycap.htm#37
The new CBA has restricted the ability of teams to "steal away" RFAs from teams lacking cap space, as happened with Gilbert Arenas. Basically the first-year salary that can be offered is capped at MLE level, but the numbers are complicated.
However,
http://members.cox.net/lmcoon/salarycap.htm#36
explains that restricted free agency applies to "veteran (i.e. non-rookie) free agents who have been in the league three or fewer seasons." So this would include both second-round picks and undrafted players.