Ok sounds like you are a bit confused but it's ok, the CBA is very complicated.

First off, as others have said, bird rights transfer with the player in a trade, as long as they have 3 consecutive years with the prior team. Any player we would trade for we will be able to offer a 5 year max with 7.5% yearly raises up to 30% of the current salary cap (other teams can only offer 4 years, 4.5% yearly raises at 30% of cap).
As for our own players. If they have 3 years with us, we can offer the same 5 yr offer above to any or all of them. We can also go above the salary cap to do so, up to an unlimited ammount, although above the luxury tax things get quite expensive fast.
One thing you are confused on though is the if we can match any offer. This privilege is only extended to teams with player who are restricted free agents (usually just finished their rookie 4 yr deal but there are some odd exceptions). This would mean only Smart, Rozier, Mickey, RJ Hunter, Young, Olynyk and all our rookies we sign this year will eventually have matching rights.
Hope this helps!