Regarding wearing cap of any form by a Muslim, Dr. Salah As-Sawi said

‘Wearing caps is not one of the peculiar features that distinguish non-Muslims from the others, therefore, there is no harm in wearing them either made of plastic or any other material. It is worth mentioning that it is more appropriate for a Muslim to wear familiar clothes that his people wear.

As for the prohibition of wearing trousers below the ankles, scholars are unanimous to the effect that it is prohibited if they are worn in arrogance. If the intention is devoid of any arrogance scholars differed, but if a Muslim is able to avoid making them go below the ankles them it is preferable so that he gets rid of the scholars’ differences of opinion.

As for letting the beard grow, it was the practice of the best Prophet (blessings and peace of Allah be upon him) regardless of whether non-Muslims do that or not.