Learn English – “I was doing something” with present perfect

You should use the appropriate tense at each point. You start talking about the summer in the past tense. No problem here.

This summer was horrible, I didn't even get to go anywhere.

Next you change to the present perfect. That's not an error. But the use of the word struggling is awkward, it looks like translationese. Better to use past tense for the accident and present perfect for your current state:

My brother had an accident, and we've been helping him recover.

"B" can also use whatever tense is appropriate. First sentence is about the past, so past tense. Second sentence is about the present, so present tense. The "I'm loving" is casual (continuous tense of stative verb), but I think acceptable here

We did loads of things and I had lots of fun. Like now, for example, I'm in New York! I'm loving everything about it.

A sentence can have mixed tense:

Yesterday I went shopping, as I will go to a party tomorrow and the bag that I had bought to take with me was too small.

Each finite clause has its own tense, and while jumping around tenses too much is confusing for the reader, and bad style, it is not incorrect.

It depends on the context/timing as to which would be most suitable but both are grammatically correct.

"Have you forgotten it again?" is present-tense and likely used in the scenario where the act of forgetting is being discussed now.

"Did you forget it again?" is probably likely to be used colloquially, it's more suited to a historic reference - i.e. the act of forgetting is in the past and it's being discussed in the present.