"COULD HAVE FINISHED" vs. "COULD FINISH" in a conditional sentence.
QUESTION:

Is the use of both [COULD HAVE FINISHED] and [COULD FINISH] correct, and are my interpretations correct?

SENTENCES:

Sentence #1 is about a future possibility, whereas sentence #2 is about a future impossibility.

1. I [COULD FINISH] the work by next Monday if I didn't have to do so many other things before then. = It is possible for me to finish the work by next Monday provided the number of things that I have to do before then is reduced.

2. I [COULD HAVE FINISHED] the work by next Monday if I didn't have to do so many other things before then. = It is impossible for me to finish the work by next Monday because I have to do so many other things before then.

Question

"COULD HAVE FINISHED" vs. "COULD FINISH" in a conditional sentence.
QUESTION:

Is the use of both [COULD HAVE FINISHED] and [COULD FINISH] correct, and are my interpretations correct?

SENTENCES:

Sentence #1 is about a future possibility, whereas sentence #2 is about a future impossibility.

1. I [COULD FINISH] the work by next Monday if I didn't have to do so many other things before then. = It is possible for me to finish the work by next Monday provided the number of things that I have to do before then is reduced.

2. I [COULD HAVE FINISHED] the work by next Monday if I didn't have to do so many other things before then. = It is impossible for me to finish the work by next Monday because I have to do so many other things before then.

Answer

Sentence number one is correct, and the interpretation is correct too.

The second sentence and interpretation are slightly incorrect. "Could have ___" is PAST tense.

I could have finished my homework if I had not been interrupted. (But I did not finish.)

"Could finish" from the first sentence could also be used to talk about a potential that is possible with no comment on whether it actually will happen.

I could finish that whole bowl of ice cream.
(You don't know if I will, but I am able to.)

Answer

Anyway, thanks Josh!

Answer

The version with "could have finished" was created by a native speaker. Here's the link: 
https://www.italki.com/question/412812

Answer

Both slightly incorrect. The first should read “I would finish the work by next monday, but I have so many other things to do before then.” and the second is actually past tense, so it wouldnt make sense to say next monday, you would say “I could have finished it, but i had so many other things to do”