Yes $30, plus a one-time $1 fee for a new card. If the Metrocard expires or is damaged the new one does not have a replacement fee. You also have to go through a turnstile upon exiting the subway, but you do not have to swipe the card again (no tap-out).
Here is the official MTA word on train frequency:
"In general, trains run every 2 to 5 minutes during rush hours (6:30 - 9:30 a.m., and 3:30 - 8 p.m., Monday through Friday), every 5 to 10 minutes during the midday (9:30 a.m. - 3:30 p.m., Monday through Friday), every 5 to 15 minutes in the evening (8 p.m. - midnight), and about every 20 minutes between midnight and 6:30 a.m."
This is of course line dependent, the busiest lines will have the more frequent service, it may seem like you are waiting forever for an L, compared to a Times Square shuttle.
Also note that at late night expresses will run local, for example an A will make all stops and there will be no C service. Late night is around midnight to 6am or so.
There have been no Amtrak trains from Grand Central Terminal since ~1990, just commuter trains since then.
Some (older) New Yorker's still refer to the subways by the IRT,IND,BMT nomenclature. IND = Independent subway, IRT = Interborough Rapid Transit, BMT = Brooklyn Manhattan Transit. Here is the translation table:
1,2,3,4,5,6,7,9, Times Square shuttle = IRT
A,B,C,D,E,F,G,Q = IND
J,L,M,N,R,Q, Franklin shuttle = BMT
If you travel on the system, check with the station agents for a copy of 'The Map'. They are free, but some stations seem to give theirs way quicker than other stations. Note, only major stations will have station agents. wf.