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The developers of stockfish and lc0 (and the many weaker engines around) would disagree, we've seen their strength improve considerably over the last few years.

Currently there's a very interesting war between small neural networks on the CPU with high search depth alpha-beta pruning (stockfish NNUE) and big neural networks on a GPU with Monte Carlo search and lower depth (lc0).

So, while machines beating humans is "solved", chess is very far from solved (just ask the guys who have actually solved chess endgames with 8 or less pieces).

Stockfish and lc0 would always draw if they are not put in unbalanced starting positions, the starting position will be swapped in the next game to make it fair.
In classical controls (what TCEC mainly uses), yes. They can play pretty exciting bullet chess without a forced opening though.