(1) 'Ain't I?' is an alternative, but ONLY for those people whose way of speaking includes the non-standard form 'ain't'. It is not an alternative for speakers of standard/ 'correct' English.
(2) We tend not to use full forms for tag questions. It isn't just a question of formality. All the examples you give, which are using modal verbs, sound very stilted and unnatural. You might come across them in a Jane Austen novel, for example, but we wouldn't normally use them in modern everyday English.
In general, we prefer to use modal/auxiliary negative contractions in tag questions. The only exception is the negative of 'am I?', which is a little different because it has no standard contracted form. By the way, I said no 'standard' contracted form, because, in fact, the form 'amn't I?' does exist - but it is only used in Scotland and Ireland. The form which has become widespread in England is the irregular 'aren't I?'. This is based on a dialect from certain English regions in which the first person singular of the verb to be is 'are', rather than 'am'. People who try to avoid this form choose to use the uncontracted form 'am I not?', because it seems more regular. But this is the exception rather than the rule - for all other subjects, we generally use the contractions.