[futo] and [tsui] do not always have negative connotations
whereas [ukkari] implies more regret, or that the action was done carelessly.
whats the difference with いきなり or 突然？
hmm this is a very good question... Let me think.
ふと would be used in the sense of "incidentally" or "by some unexpected turn of event." It is more or less an unexpected thing that catch you more or less passively. いきなり and 突然 has the connotation of "out of blue" or "abruptly" so that there is a big element of surprise.
what is the difference with 偶然 ?
偶然 「ぐうぜん」 I think means more what a coincidence. As in "what a surprise to see you here!" 突然 「とつぜん」is more similar, like "out of the blue". いきなり is another similar word. いきなり結婚した - got married all of a sudden
For me, there are hints (like endling と) for the word is an onomatopoeia construction, that's the difference... As in, 「ふと気がついたの。」"'Pooh!' - the realization came." Although it's not as childish in Japanese, as they use onomatopoeia words a lot.
Yes. Bamboo4 is correct. 3940 should start "Incidentally, "
Kaens へ I don't think ふと、is not an onomatopoeia construction. In kanji 不図 not planned, not mapped, unexpectedly, etc. I don't know why they don't write it in kanji though, as both are easy...