It depends on context. Here are some examples:
Last week I was repairing my car.
That does sound like you were repairing the car throughout the week. It could mean that it took the whole week, most of the week, or that it just spanned the entire week (perhaps with breaks in between or it was done alongside other tasks). As a complete sentence, without any other qualifying information, it sounds like a description of what occupied your time 'last week'. If you wanted it make it clear that the repair took up all of that time you should qualify it by saying something like "all of last week I was repairing my car".
Last week, I was repairing my car when I hurt my hand.
In this example, the setting for an event is 'last week'. That could mean any time in the last calendar week, or perhaps one full week (7 days) ago. It does not mean that either the repair took a week, or even a full day, just that the repair took place at some time last week and the hand incident occurred while the repair was taking place. It's an incident, within an event, within a time period.
To briefly address your second point (questions are really meant to be about 1 thing), "I was working there for 2 years" because it is a logical statement about something you were doing, and for how long.
The sentence "when I was little I was going to school" doesn't sound right because it's full of ambiguity and repetition. "When I was little" is a very vague time period, although that works fine for an anecdote where the exact time is of no consequence. It also repeats the subject and verb from the previous clause, so it just sounds rubbish. A better throwaway statement would be "I went to school when I was little". Of course, as in my example earlier, you could make the time frame a separate clause if you were expanding on the second, for example "when I was little, I was going to school one day when [something happened]".