tapa-niya comes from the word for strong glowing and burning heat, like that of a big fire or sun. It also means the practice of self-torture done by the yogis. So I suppose metaphorically it refers to blaming oneself, torturing oneself, "giving oneself a heat", "beating-up oneself".
vi-ppati-sara I think means something like "acknowledge result of one's wrongdoing", "realize one's mistake", "admit responsibility", "take blame", "plead guilty", "repent" etc.
So both tapaniya and vippatisara can be used to indicate regret and remorse - but one emphasizes the self-blaming aspect while the other emphasizes going back in time to look at one's past action.
Udhacca-kukkucca, as I explained in another answer, indicates something completely different -- obsessive wavering about right/wrong action, a scruples. While the previous two words pertain to someone experiencing results of one's past unskillful action, this one pertains to someone's state of worry and anxious wavering while choosing a course of action (including the no-action), even if it's actually the right choice.
Note, that Udhacca-kukkucca is completely different from 'vicikiccha' which is generic scepticism about something external, not anxious wavering about one's action.