That would make a fine fixed gear bike.

You can soak the bottom bracket in a solution of oxalic acid in water to remove the rust and it won't harm the paint. If the stem is stuck, a long pipe on the end of your wrench, another pipe onto the end of the stem, and a couple of friends to hold the frame while you give the wrench a good pull or push should do the trick. It helps to use penetrating oil a day or so before. Pour an ammonia solution into the downtube from the bottom bracket and rotate the frame so the solution can contact the stem from the inside of the frame. That will dissolve some of the aluminum and corrosion that is keeping the stem stuck.

Even if the stem isn't stuck, you should remove it and replace the bearings in the headset and apply fresh grease.

A bike shop will have a tap that will match the bottom bracket threads and they can use that to "chase" them. Cleans them up so the bottom bracket cartridge will fit nicely.

Please post pictures of the bike when you finish it.