The question seems to focus more on religion than on sports or hair style.
A religion is a practice not a belief. You might not believe religions exist until you see people go to a place of worship. So religions are a fact, not a belief. They do exist.
However, a religion's followers share their beliefs in theological matters.
So if you see someone reading a holy book, pertinent questions might be
Do you follow a religion?
Do you practice a religion?
Which religion do you follow?
But if a conversation has given you a hint that it may be so, you can ask
Are you religious?
I would not use that as an opening line for a conversation, it needs to be led towards by "small talk" to get a conversation going, unless you have an encounter with someone reading a holy book.
I realise I have side-stepped the question about "a" or "any", because I would not say it like that at all, and I hope this answer helps.
Update:
In the second case, I think you can say "a team" or "any team".
The third case is harder.
Is there a girl with weird short pink hair at the party?
This implies you have seen or know the girl and want to know if she is at the party.
Is there any girl with weird short pink hair at the party?
This means you want to meet such a girl and ask if there is one like her at the party.
Best Answer
1) Never in my wildest dreams did I think I could actually pass the exam.
2) Spoken language: Never in my wildest dreams did I think "I can actually pass the exam". [quoting oneself]
And the "I can actually pass the exam" would be given air quotes in speech or a change of tone when speaking it to show it is quoted within an utterance.
3) Never in my wildest dreams do I think I can actually pass the exam.
That is how I would write them. Unless you part about passing the exam is quoted within the utterance, it has to be either in the past or in the present: can//do and could//did.
My answer is the same as the other except with regard to handling the quoted part.