Day Questions

I wish to adopt a child. Is this permissible? If so, and I adopt a boy, does my wife have to keep the hijab on in front of him? Similarly, if I adopt a girl, will I be prohibited from looking at her without hijab?

It is permissible to adopt a child, and with adoption we mean providing for and raising a non-Mahram child. However, he or she remains a stranger to the family, so wearing hijab is obligatory as you mentioned in the question.

I find that I discharge a thick liquid resembling pre-ejaculatory fluid whenever I urinate. Do I need to remove it or make the place tahir?

This substance is not originally najis. but when it comes in contact with urine it becomes najis. You should wash it in the regular conventional way, and there is nothing further to be done.