Pallet Grandpa finalization fail

[Mr-Leshiy]

I am learning how the grandpa works, and I have found a few interesting things.

1. When I have added two accounts as a session_keys in the chain_spec.rs (Alice, Bob) and run only one substrate node where I have inserted both keys for the Alice and Bob. So block producing did not fail and blocks has been being produced by Alice and Bob in turn, but finalization failed and no one block has not been finalized. And such problem was fixed just running two nodes separate nodes with Bob keys on the one node and with the Alice keys on the other node. So the question is why it is impossible to finalize blocks from two accounts on the same node, but block producing works ?
2. Such problem connected with the first issue. I have modified new_session method of the pallet_session trait and return new validators set. So I have the next case:

• on the start of the blockchain I have 2 validators Alice and Bob, which have been added to the chain_spec.rs.
• finalization did not work due to reasons described below, block producing worked
• on the height for example 20 I have changed the current validator list, so the new validator list contained only Alice, new the only ONE validator was Alice at that step.
• finalization still did not work, block producing worked and blocks have been produced by only Alice.
• I have changed the power of the validator Alice in the grandpa for the amount 100 instead of the 1 (it is the default value) and I expect that this should help and finalization should start work, even with the one node, because the current validator had more than 2/3 of the power stake. But the finalization still did not work.
  Can you also comment on this how should it works ?