With your additional information, I would say replace by next spring, or next autumn at the latest. The cracked portion inside the pool can wait until you replace the liner.

Adding the self leveling to the cracks may not be a good idea, however it MIGHT buy a short amount of time. Not much though, so it might not be cost effective. I don't know if it would damage the coping or liner.

When you have it done, Check with your local concrete mixing plant -- the guys with the trucks -- about recommending a contractor that would be familiar with this type of work.

When you get a few contractor names, ask each of them about the feasibility of either frost wall footings or thickened edge slab for the outer edge, away from the pool. Being that you are from fairly cold country, my bet is that a frost wall footing would be best, for ground stability. There will be extra cost in doing this, but think of it as cheap insurance against this happening again. The frost wall needs only be a 4 - 6" wide trench cut into the ground near the outside of the deck, with rebar to tie the footing to the deck. Personally, I'd widen the deck about a foot or so while I was getting this done.

Again, have them place 3/8" road base, compacted, under the slab.

For removal, yes you could do that yourself, with a little labor help. Electric jackhammers are relatively inexpensive to rent. With 1 or 2 of them, you could have the deck at least broken up in a couple of hours if not hauled out to the skip.

Good luck!