Soak the BB cup with Liquid Wrench (or similar), let sit while it penetrates, then clamp the flats on the cup in a decent-sized bench vise and use the leverage of the whole frame to unscrew. Keep in mind that the right cups are likely reverse-threaded, so you need to spin them clockwise to remove them.
For the seatpost, try the same method listed above, clamping the exposed section of seatpost. Crushing it will be necessary, but be careful not to break it making it useless.
No luck? Try heating the post with a propane torch until it's glowing dark red under the flame. Carefully re-apply penetrating oil, and try clamping and twisting again.
No luck? Let cool, cap the top of the seatpost with duct tape, flip the bike over, pour household ammonia down the seattube through the BB shell, and let sit overnight. Drain and try the clamp & twist thing again the next day.
Try a blow torch or similar on the cups and the seat tube.
Wont matter as your going to weld them so need to strip the paint
I lightly hammer the cups. Flat on the face of them. To break the bond of the threads.
Then A chissel with a hammer to drift them round. A big flat blade screwdriver instead, if you dont have a chissel.
If the seat pin is steel. I would fit a bolt thats a good tight fit in the remains of the seat post. Then clamp the post in a vice really tightly. Then try to turn the frame on the seat post. Oiling and or heating it is good. May make a very disconcerting creak noise. But ussually comes out. Is heavy work though.
Sometimes there too stuck in though. And just tear to bits when I do that.
If you don't care about the condition of the cups after they have been removed, I've had excellent luck placing a cold chisel against the edge of the square boss (near the outer diameter of the cup) and hitting (not tapping) with a large hammer. Works every time. Just be sure that you are turning the cup in the correct direction with the hammer blows. And wear safety glasses. When it does finally turn out enough to expose some threads you can then use either channel locks or a pipe wrench for the rest of the job. Ugly but effective.