"I wish I hadn’t bought this watch BECAUSE it is always stopping."
"He regrets that he (had) bought it" -- More likely without the "had"
"I wish I had bought this watch" -- Fine
"He regretS [or"regretted"] that he hadn't bought it. ?
"She really wished she’d stayed on at college." - good
"She regretS that she hadn't sTayed on at college." -- You can omit "hadn't" for the positive or you can substitute "didn't stay" for the negative, but they all mean different things.
"She really wished she hadn't stayed (on) at the party. ".
"She regretS [or "regretted"] that she had stayed on at the party?"
I think you are mostly struggling with whether to use past tense or a pluperfect construction for the the regrettable event. If the regret was in the past, use the pluperfect. When the regrets are in the present and something happened in the past, it is usually a simple past you should use.
"Wish" isn't so much a negative construction as one that is contrary to reality. It takes a past tense in examples like these: "I wish I stayed" or "I wish I could" or "I wish I was/were". That last one is a bit tricky. Because you aren't (whatever), it is contrary to fact, and you will often see a so-called past subjunctive, especially in US English, so "were" rather than "was". There's no difference for any verbs other than "be" and then only for 1st and third persons singular. Consequently, this use is dying out, especially in the UK, and you'll often see "was" here. However, this is the kind of thing that some teachers (in my view inordinately) care about, and you will be safer with "were".
Finally, "He was sacked because he had been stealing money" probably means he stole on multiple occasions. Otherwise, if you really don't care how times it was, you would simply say "He was sacked because he had stolen money".