Oh yes, after the 10th beer it is very difficult to distinguish between the two :-)) .
It is one. I didn't know pajamas also came in pairs. They are like pant suits. Why aren't pant suits in pairs then? :)
Anyway, "egy pizsama" is something that one person can wear at a time. As a general rule, for any piece of clothing or accessory: if it is one piece, it is singular in Hungarian.
Pyjamas is English spelling, yes. Plural, because there are two parts i suppose. What i would call a "trouser suit" would be singular because "suit" implies two pieces ( also just womens clothing, men would just wear a suit). If there was also a waistcoat, that would be a "three piece suit" and that would be for men.