Learn Italian: Non ce la faccio più con queste chiamate! - I can't take it anymore with these calls!

It comes from the special verb farcela, which means to manage, to succeed, or to cope. If you just used faccio (from fare, to do), it would mean I don't do anymore, which does not make sense here. Farcela is the verb you need to express that you can't take it or can't cope with a situation.

What exactly do the words ce and la mean in this sentence?

In the verb farcela, the ce and la are fixed pronouns attached to the verb fare. They do not translate directly to us or it like they normally would. Instead, they just combine with the verb to create the new meaning of managing or coping. When you conjugate the verb for I, they split off and go in front: ce la faccio.

How do we get the meaning anymore in this sentence?

The combination of non before the verb and più after it creates the meaning not anymore or no longer. In Italian, you frame the verb and its pronouns with them: non ce la faccio più means I can't take it anymore.

Why is it queste chiamate and not questi chiamati?