+0
Even though those are the very basics, I am forced to ask you about the correctness of the particular sentences below, because I am not sure myself.

(1) Finally I've come home today. - I dare say this one is incorrect, isn't it? Although the time specification "today" is not finished yet, I would use past simple. Is anyone capable of giving me a sufficient explanation?

(2) I've done a lot of work today. - Past simple or present perfect? I incline more to PP here.

(3) In the past four days I've been very tired. - Correct or?
P.S. Is the word past here interchangeable with last?

Thank you very much.
+1
(1) Finally I've come home today. - I dare say this one is incorrect, isn't it? -- This is 'correct' and very common and natural.
(2) I've done a lot of work today. - Past simple or present perfect?- Both are fine.
(3) In the past four days I've been very tired. -- Fine.
P.S. Is the word past here interchangeable with last?- Yes.
Comments  
Site Hint: Check out our list of pronunciation videos.
Thank you very much for your direct and plain answers.

And please, what about: "I've come home today's morning."? Is it fine?
No. 'Today's morning' is not an English formation. It is 'this morning'. And whether you use present perfect there depends on what time it is.