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It's strange though, if you switch that sentence round ("I'll do the work by this evening") it sounds much more natural. Perhaps it's because it's like a promise here ("I promise you, I WILL do the...

Bear in mind that I'm not a qualified teacher, I'm just an ordinary English speaker, so it's possible your teacher knows more than me. It may be acceptable to use future simple, but it certainly...

By the evening I'll have done the work = correct. When you say "by X time", you use future perfect. Don't say "by the evening I'll do the work".

Similarly with your other two examples - use future...