They are similar but not interchangeable. A person can manage a team. A person does not “handle” a team. (This sounds very forceful) We handle problems and situations. Handle means to hold (weight), to deal with, or even to take care care of. Manage means to oversee or to be able to do something. Example: I managed to pass my test, even though I didn’t study. Here you would not use “handle”

Not necessarily. Although the meaning is the same, you can't just use them interchangeably. For example.....

A: there's a lot of work to do

B: yeah, but we'll manage

If B were to say "yeah, but we'll handle". It sounds a little strange. I would say instead "yeah, but we'll be able to handle it", or even "yeah, but we'll handle it".

Another example: a rope can handle a certain amount of weight, but it can't manage a certain amount of weight.

Although I can't give you a definitive answer on how to use these two words, I hope this helped a bit and that someone else can give you more insight on this.