I am meeting my ex girlfriend after ages today.

What does this sentence mean ?

Does it mean, I am yet to meet her today or does that mean that she is with me right now .

And also, could anybody please tell me which one of the below sentences is more natural/correct ?

I was meeting my ex girlfriend after ages and the conversation felt awkward.

Vs

I was meeting my ex girlfriend after ages and the conversation was feeling awkward.

It felt or it was feeling ? Considering that the conversation was still going on