[susan53]

1. Neutral rather than formal. But in the British national corpus on the other hand occurs 47 times in written texts, predominantly in a second sentence while it occurs 17 times in spoken texts and is predominantly combined with a co-ordinating conjunction. So it it clearly more common in written English and used differently when it occurs in spoken language. Some typical examples :

Written :
...25%, for instance, in a four- member constituency. On the other hand, the distribution of first- preference vote...
...militates against the decision- taking ability of firms. On the other hand, they are not prepared to countenance...

SPOKEN
...it could break your arm. And on the other hand, if it started and took off suddenly, ...
...they're not an executor's personal responsibility, but on the other hand an executor is not entitled to charge...



2. Still is wrong here in any case as it expresses concession (a "surprising" change in the direction of the text, breaking the reader/listener's expectations) rather than contrast - which is what is involved in your examples. Compare :
I got sea bass instead of salmon. The salmon was really expensive, but the sea bass was on special offer. but = contrast : expensive vs cheap
The salmon was really expensive but I bought it anyway as I like it better than sea bass.
but = concession. The beginning of the sentence (The salmon was really expensive) suggests that the speaker won't buy it, but then she "surprises" you by saying she did anyway.

But and However can express both concession and contrast (so are OK in your examples and in mine),
yet and still can only be used to express concession, (and so are not possible in your examples or in the first of mine)
on the other hand can only be used to express contrast (so would be OK in your examples and in my first, but not in my second).

Then on top of that you have the stylistic differences and frequency differences in spoken/written English - so Still I for instance occurs 8 times in the BNC spoken corpus and not at all in the written corpus.