If talking about computers we say "зависнуть". --- Компьютер завис or even like this though less common --- компьютер висит (as in right now and please, don't take the literal meaning for that
)
if talking about being stuck as in when speaking, that's a bit difficult because I don't think there is an all around solution for this, you need to come up with something different like:
Я не знаю, как это сказать... Я забыл слово... Я не мог говорить связно (like I couldn't come up with something comprehensive, because of the lack of vocabulary or something else, or couldn't tie up words or sentences into something that would make sense.)
3) That actually depends on what you mean with the bit, because I think we'd usually name the bit with the word that bit really is. Like:
Do you want me to put this bit on your bracelet, to see how it looks - Хотите, чтобы я прикрепил этот камушек на браслет, чтобы посмотреть как он будет выглядеть с ним?
I will show you how to put on the bit on your bracelet - Я покажу вам, как прикреплять/прикрепить камушек на браслет
Note: under "камушек" I mean a gem.