There are several possible contractions, none of which are acceptable to all speakers. The only thing that is fully acceptable to everyone is am I not?.
The contraction amn't is used only in Scottish and Irish English. Most North Americans have never heard it, and unless I'm mistaken, most English people readily identify it as Scottish.
The contraction ain't I? used to be acceptable, but because of the condemnation of he ain't for "he hasn't/isn't" and other uses of ain't, the phrase ain't I? became tainted by association. Now you can't say "ain't I?" without sounding uneducated to many people. This probably sounded more acceptable three or four generations ago than it does now; language commentator William Safire still recommended its use in 1982.
In southern England people began saying something like an't I? in the late 17th century, pronounced ahnt. Because the southern English drop their rs, they later started spelling this as aren't I, with no difference in pronunciation. They preferred to use an unrelated word whose written form was familiar to them and whose pronunciation was the same.
When American r-keepers began noticing this in British writing at the beginning of the 20th century, it sounded crazy to them to have an r there. It made no sense at all, because there was no connection with the word are. So aren't I attracted considerable criticism. Nonetheless, it has gained acceptance over time, and now most Americans use it, since it's the only contracted form available to them that doesn't involve ain't.
Nowadays you'll find contradictory opinions on the acceptability of aren't I in writing, and particularly in formal writing. If you want to avoid controversy, stick to am I not? in writing. (The advice might differ if you're writing in Standard Scottish English, but I'm not qualified to comment on this.)
In speech and in writing meant to remain close to speech, there is a danger, alluded to in the comments, that am I not? will sound excessively stuffy and formal. In this case, aren't I? may be preferable, at least in England and North America.
No matter where you put the "not", a statement with "to had" isn't grammatical. The construction you are using is "seem" + to-infinitive. The infinitive for the verb have/had is "to have", not "to had."
This is discussed in detail on the BBC "Learning English" website:
seem / appear to + infinitive
After seem and appear we often use a
to + infinitive construction ( or a perfect infinitive construction
for past events).
...
So what you should say is either of:
He seemed not to have understood what I had said to him.
He seemed to have not understood what I had said to him.
He seemed to not have understood what I had said to him.
The "not" could really go in any of those 3 places, but the first possibility sounds smoother and more idiomatic. The last sentence sounds the least natural to me, even slightly awkward.
Best Answer
Ending a sentence with a contraction is entirely valid in normal English.
In fact, in the above, use of the non-contracted forms instead of the contracted-forms sounds stilted, although your point will still get across.
Note that there are some contractions where, as Bill points out in the comments below, one would not normally make use of them at the end of a sentence: