Not really a huge deal since people should just install Fallout Fixt for Fallout 1 anyway which you can get at Moddb: http://www.moddb.com/mods/fallout-fixt/downloads
No, they shouldn't, since it's buggy.
In my experience using the TeamX patches is much safer.
It contains everything listed in the OP in one convenient installer.
And then some...it adds too many things, some of which introduce too many bugs.
Fixt is still in Alpha.
Have you actually used FIXT or even read about it?
1) Bugs aren't really an issue. I've not encountered any and I've played every year for a several years through a couple of versions of FIXT (and I've lurked the creator's thread at No Mutant Allowed so I've seen people post some bugs, plus he has a link in the first page to the wikia where he lists bugs and if they aren't fixable - and why).
2) So then, don't install the extra stuff? Download the Fixes-only version or go ahead and download the full custom version because there is a purist (fixes-only) version for you, a Standard (half-purist, only some new stuff), and then full blown - everything version. In addition, the full custom version has a customize option so you can choose and change what you want/don't want.
3) Alpha, so? It's content complete as far as what he can do with it as far as Fallout 1 goes. It's considered Alpha because he's now working on getting it so it ports Fallout 1 into the superior Fallout 2 engine. But it can be considered complete because the creator has fixed all the bugs he can in Fallout 1 (iirc some of the bugs left are because of the engine Fallout 1 uses and the port to the Fallout 2 engine should help fix those).
So, Fallout FIXT is still the way to go to patch Fallout 1 because other than you, I've not head people complaining about it. First time players can (and imo should) just download the fixes only version and not have to worry about any possible bugs added by the new things as you suggest.