No, because "The employee has jobs." would mean that the person we are talking about (i.e. the employee) has several jobs.
"Personalul are slujbe." may not be the most meaningful/useful sentence, but the translations "The personnel has jobs." and "The staff has jobs." seem to be the best for conveying the original intended meaning.
Well, that's a finer nuance in the English language. Seems that both can be used, but "has" (singular) is preferred in American English, while "have" (plural) is preferred in British English. See the accepted answer here. It applies equally to "personnel", "staff", or any other collective nouns.
Hmm, this is interesting to explore. I'm an American and when referring to the personnel as a collective unit, I would say things like "the personnel has a lot to do." But if I'm talking about the personnel as a set of individual people, I would say "our personnel have many different roles." I would still translate this sentence as "the personnel have jobs" even though I'm not British.
I believe it is stronger than a preference in British English. I checked the examples on the oxford dictionaries site and they all take the plural verb if it is conjugated rather than being a subjunctive/infinitive. The idea of using a singular verb after the word grates and I have American relatives but don't think I ever heard them use it as a singular either. Other collective people words such as team do get used both ways, and my feeling is that it depends if they are acting collectively or in some way individually - so the team is selling coffee but the team drive cars here it is a group of people acting individually...