With a aluminium frame it would be a very bad idea to use caustic soda. It will eat way at the seatpost but it will also eat away at the frame.
Caustic is fine on steel frames, although it does strip paint too, but it's very damaging to aluminium.
Turn the frame/bike upside down, take out one of the bottle bolts on the seat tube and pour plenty of PlusGas
penetrating fluid in so it fills the seatpost area.
If the bike has no bottle bosses on the seatpost (which it looks like it may not) then you'll need to remove the chainset and bottom bracket to pour in PlusGas from there.
Leave it to soak overnight and then try again by twisting the saddle and seatpost. Once the corrosion breaks then it's fairly straight forward to remove the post.
Whatever you do though, don't use caustic soda...
Oh and a 9 speed Deore set up would work fine. Plenty of good functional Deore stuff about on ebay to be had for not very much money.
It looks like your front brake lever and hydraulic hose are damaged too though.