Interesting experiences

'could of' (Answer 1) is a common ~ and wrong, however widespread ~ substitution for 'could have'; Answer 2 contains more prissy conditional/subjunctive/modal forms than clear English really needs, and 'would have arrived' (with its sense of the past) is inappropriate here; Answer 4 is possible but perhaps too simple.
Answer 3 balances more clearly and elegantly than any of the others.

Believe it or not, Answer 1 is fine; each half of the repeat carries a slightly different sense, but the words themselves work equally well both ways.
There is no need for 'that'/'when' or any form of subjunctive; English is perfectly clear without any such devices (unlike several other fine languages, possibly including yours!).

The Present forms (Answers 3 & 4) are wrong here in reference to a past event; if it was a single event, the continuous / imperfect tense (Answer 1) feels wrong too.
Meanwhile 'dreamt' is a permissible alternative to the 'weak' form 'dreamed' (as in: 'I never dreamt there would be all this trouble/traffic').

It will have been the final First Prize. The verb should be in the past tense (Answer 4, rather than 3) since 'that' suggests that the speaker has already let go of, and passed on, the prize.

' ... an occasion WHEN ... ' , rather than 'that'.
If there hadn't even been one such occasion, there can be no need for a continuous tense (Answer 3).

' ... have made ... ' suggests the recent past (of the latest occurrence), and that there is a sense of continuity or repetition about how it's been happening.
Answer 1 is wrong, if still more or less clear English; Answer 2 is more an American usage; the present form (Answer 4) is not good English, even in context, and more probably reflects a different, foreign usage.

The context suggests that the speaker is either finishing the drink, or possibly just about to start (or even buy) it ~ with the use of the Present Continuous to imply imminent future action.
The plain present (Answer 1) would be understood but isn't natural here; Answer 3 is possible but, again, somehow slightly less natural in context; despite 'last' suggesting something being past or finished, the past tense in Answer 4 is also wrong here.

We need the Pluperfect (Past Perfect) here since the paintings date from two steps back into the past; English usually speaks in terms of 'doing' rather than 'making' a painting (possibly because 'make' somehow suggests an artefact in three dimensions, rather than a mere two).

' ... chance of being ... ' is probably a little more natural than ' ... chance that something is ...' (Answer 1).
'Was' (Answer 3) is clearly wrong in this theoretical context; meanwhile Answer 4 is misconstructed.

It may be the 'last time', but not until 'next week' ~ so the past tenses (though tempting) in Answers 1 & 2 won't make good sense.
The apparent Present Continuous (meaning future action) in Answer 4 is best; Answer 3 is possible but rather abrupt, even from someone who presumably has other important matters on their mind.