I am in the process of converting an old Peugeot, which seems to be of a similar era to yours (80s?). Nice thing about mine is that it has a high BB, so great for a fixie, although I see you are going single speed, so not such a benefit for you.
Some thoughts:
Bottom bracket:
i) Great article about BB removal on Sheldon Brown's website: http://www.sheldonbrown.com/tooltips/bbcups.html
I reckon bench vice is probably the way to go, but you may want to take your frame to your LBS and get them to try to get it out.
ii) Big watch out with old Peugeots. They used to use French threaded BBs (70s and very early 80s I think) and it is harder to get replacement (cartridge) BBs for those, so if yours is French threaded, you may want to clean, regrease and keep your one. I am lucky - mine is late enough to be British threaded, so I can put in a new cartridge (handy, since I've lost all the old bits of the BB).
Stem:
By "strip the allen bolt", do you mean that you made the hole that you put the allen key into circular so allen key no longer works, or do you mean that the bolt has sheared off (snapped in two). If the former, you may need to get the head of the allen bolt drilled out of the stem (find a local machinist workshop to do this for you if you do not have the appropriate power tools). If the latter, you should be able to poke a long rod of appropriate diameter down the stem hole and wallop it with a hammer to release the stem locking thingumajig.
Seatpost:
Peugeot's of that era seem to have very narrow seat tubes. Mine is 24mm. Seatposts of this size are hard to come by. I ended up getting one from Decathlon (called L330 or something like that) - costs a tenner. Comes up slightly too narrow (23.4mm), so I created a shim for it with a very thin sheet of metal which worked a treat (can give you more details if you are interested).
robadob.
I am in the process of converting an old Peugeot, which seems to be of a similar era to yours (80s?). Nice thing about mine is that it has a high BB, so great for a fixie, although I see you are going single speed, so not such a benefit for you.
Some thoughts:
Bottom bracket:
i) Great article about BB removal on Sheldon Brown's website:
http://www.sheldonbrown.com/tooltips/bbcups.html
I reckon bench vice is probably the way to go, but you may want to take your frame to your LBS and get them to try to get it out.
ii) Big watch out with old Peugeots. They used to use French threaded BBs (70s and very early 80s I think) and it is harder to get replacement (cartridge) BBs for those, so if yours is French threaded, you may want to clean, regrease and keep your one. I am lucky - mine is late enough to be British threaded, so I can put in a new cartridge (handy, since I've lost all the old bits of the BB).
Stem:
By "strip the allen bolt", do you mean that you made the hole that you put the allen key into circular so allen key no longer works, or do you mean that the bolt has sheared off (snapped in two). If the former, you may need to get the head of the allen bolt drilled out of the stem (find a local machinist workshop to do this for you if you do not have the appropriate power tools). If the latter, you should be able to poke a long rod of appropriate diameter down the stem hole and wallop it with a hammer to release the stem locking thingumajig.
Seatpost:
Peugeot's of that era seem to have very narrow seat tubes. Mine is 24mm. Seatposts of this size are hard to come by. I ended up getting one from Decathlon (called L330 or something like that) - costs a tenner. Comes up slightly too narrow (23.4mm), so I created a shim for it with a very thin sheet of metal which worked a treat (can give you more details if you are interested).
Good luck with your project!