While you can get fired from your internship for asking too many questions, its generally not going to happen, and you'd be aware you were on thin ice well before that point.
Given that, you note:
However, these days there is no tasks assigned to me all day and I end up doing nothing in front of the computer all day. I will sometimes get work to do only if I personally go to certain lawyers that I've been assigned tasks before for more work.
While this is awkward for you, and possibly a little annoying for them, you have to keep doing this. From their point of view, they probably don't delegate that much work, so they'll be as new to this as you are to asking for work.
But what they will see is someone who wants to learn and is working hard at it. That is a pretty useful trait to have, so there isn't much wrong with it. While you're not involved in this firm's particular area of expertise, you can still learn it, or learn the process of running/working in a law firm.
Actually, I know this is not even vaguely your area of work, but you might be interested to look at how they do their book-keeping and billing, or note what areas of industry their clients work in. Law firms, because they're so closely engaged with their customers, can shine by offering not only legal advice, but also understanding the business implications of their clientele.
An example might be an IP law firm - yes, they can write your patent application, but it would also be useful if they could provide advice/considerations on if the patent is worth filing. Similarly for lawyers acting for newly funded companies, an understanding of what a startup goes through would be useful.
You might benefit from, if you don't have any legal work to do, in learning about the most common industry this firm services. If nothing else, and if you truly cannot get any work to do, or for those days where nobody can give you any, a summary of the industry and the legal problems it generally faces etc would be useful for your firm in the next week.