It's OK, but it would be better to link the two statements. For example: Avoid wearing clothes made of artificial fibres, as they cause allergies. 'Fibers' is the US spelling, 'fibres' the British one.

Yes, that is correct. I think it should be a semicolon instead of a comma though. That is, Avoid wearing clothes made of artificial fibers; they cause allergies.

There are a couple of things I would suggest to improve it. I would use 'made from' instead of 'made of'. I can't really explain why, but to me it sounds better to use 'made from' in this instance. I would also say 'can cause allergies.' The way it is written it sounds like artificial fibres always cause allergies, which isn't the case. And as you may have just noticed fiber is the American spelling. Avoid wearing clothes made from artificial fibres, they can cause allergies.

Yes, in my opinion this sentence is correct.