Well, having to rev it to get the alternator to start charging is probably related to a loose belt. I have had that same condition on more than one Fiero. The best solution I have seen is rodneys idler pulley. Considering that this is your low mileage 87 we are talking about you probably don't want to go away from stock. The only other thing I could say is to get that belt really tight.
The reason it dies is probably related to you not driving it enough. It isn't used to running. Get it out and get some miles on it once in awhile

Seriously though when it is running without the load of the alternator there is alot less load on the engine and it dosn't take much air to keep it running thus the IAC valve is relatively closed. When the alternator kicks in and you let it go back to idle the IAC valve hasn't moved but there is more load now and possibly can't react quick enough to keep from stalling. This has also happened to me from time to time and tightening the belt such that the alternator spins and charges on startup always resolved the problem.
You don't have the stock belt on that thing still do you?
[This message has been edited by Jefrysuko (edited 08-13-2008).]