[A-2] I’ll open the window.
At the point of saying this, you already made the decision to open the window, since in effect you are agreeing it is too hot and you are offering to (want to) do it.
[B-1] I’m going to learn to play the guitar.
Here you have the intention to learn to play the guitar, but it is a long process and it is uncertain whether you will be successful or not. So this is a "present intention".
So can be used to say that another subject is doing something "as well" or "in addition." - you can keep things in one sentence with so but not with as well or in addition (so that's why it happens in speech often):
Vinay plays cricket, and so does Ashok.
Vinay plays cricket. Ashok does as well.
But if there's a second action, so takes on the meaning of because of that:
He can speak French, and so can speak German.
He can speak French and because of that he can speak German.
Don't use so at all, simply say
He can speak French and German.
The problem with this:
I seldom went to Christmas parties, neither did he.
is that while "seldom went" has the meaning does not go that often, it's not a verb in negative form, so neither doesn't correctly link back to it.
You can either change "seldom went" to a negative verb, add "he" to the subject of the sentence, or make "neither did he" a full sentence with "either". ("Seldom" is one of those words you generally don't want to overuse by using it in two sentences in a row.)
I didn't tend to go to Christmas parties, neither did he.
He and I seldom went to Christmas parties.
I seldom went to Christmas parties. He didn't usually show up to them either.
Best Answer
There are a number of ways to refer to the future in English. However, one of the sentences you suggest is clearly incorrect: you definitely should not use the "simple present" play in the first sentence. It sounds completely unacceptable to me:
The simple present is more acceptable in the second sentence than the first, but nonetheless I don't think it would be a good choice in general, only in certain specific circumstances that I can't quite pin down.
(I would use singular verb agreement with the collective noun team, but some other speakers would use plural verb agreement. Either is considered acceptable.)
One option for referring to the future that you haven't mentioned and that I think would be a good choice here is the progressive. I think both of the following sentences sound quite natural:
The present progressive can often be used like this when you have a phrase like "on Friday/on Saturday" that indicates the time in the future when the event is going to occur.
The "be going to" construction that you mentioned also sounds fine to me here:
It's also possible to combine the progressive with the future marker "will", as in the following example:
For some reason, this doesn't sound as good to me in the second sentence.