Fancy your chances?

In the likely circumstances of such a question, the speaker would be looking at the person spoken-to, so the 'you' would be almost superfluous.

The classic, laconic admission of failure!

Ellipsis like this would only work if the speaker is describing their own experience.

'Thinks' is in the 3rd person singular, so its preceding subject must be 'he' / 'she' / 'it'. In the context, and from the later repetition, the missing word must be 'he'.

There is a clue in the 'you' within the original Question.

The full instruction would be 'be careful' (likewise 'be quiet', etc.).

'There is ...' is such a 'throwaway' phrase (and like all true idioms, it makes very little sense whatever if you try to take it apart word-by-word) ~ that it is very often left off completely in situations like this, so as to move straight to the topic in hand.

'It' will be hopeless; though 'you' would also make sense here. We suspect that the 'it' version would be a bit more diplomatic; otherwise you are adding to the person's frustrations by emphasising that they are wasting their time. The indirect (or unspoken) version is probably preferable.

The speaker is leaving out his/her personal pronoun, as it should be obvious (from the situation, and by elimination) that they are speaking on their own behalf.

The word in front of the noun (microwave) would have had to be an adjective: possessive (e.g. 'our', 'your') or demonstrative ('this', 'that'); so only one of the Answers offered will work here.
'On the blink' is a slightly old-fashioned expression, though still heard at least occasionally, meaning that a ~ usually, electric ~ machine is either not functioning at all, or only intermittently (i.e. any lights on it may only be blinking on and off, rather than shining constantly).