There was an in-game time limit?
I loved Fallout 1. So much. My issue was that I got pretty far in and saved myself into a combat situation where I couldn't save my dog from dying. So I started over.
There were two time limits. The second one was patched out. The first one was left in -- you have like 150 days to find the water chip -- but it's hard to hit this because, unless you're REALLY screwing around or made a character with no int/personality, a couple NPCs in Shady Springs direct you to Junktown and the Hub, and the Hub directs you to the area where you find the chip.
wrt dogmeat, you can't tell him to stay outside during the last dungeon, so it's REALLY hard to keep him alive. I managed to by getting him stuck behind a one-way door, so the Master left him alone.
... Man, Fallout 1 was one of the few games I bothered finishing. Being really short helped.