Can I bring the eyeglasses frame to an optometrist to insert the lens into it?

Unlikely. An optician will make your glasses for you. If you have a frame you love, you can have new lenses inserted into it. But lenses are fabricated by using the old lens already in the frame as a template to cut the new lens to fit. If you just have a frame, it is very complex to put a lens in with the proper fit and most optical shops will not do this.
Certainly. By your question, it's unclear if your lens has fallen out and needs to be replaced in your frames of if you need new lenses in your existing frames. Either way, your local optometrist should be able to help you with that.
Probably. As long as the frames are in good shape and are meant to have lenses replaced, there should not be a problem. Certain lenses are glued into the frames and cannot be easily replaced. Also, some frames can be damaged in the act of replacing the lenses. A good optical shop should be able to help you out.

Related Questions

Can I bring the eyeglasses frame to an optometrist to insert new lens into it?

Usually yes. If the frame is not damaged and has a contemporary design, then usually lenses would be able to be cut by the optician to fit the frames. There are some older frames where it can be very difficult to fit lenses. Read more...