You can catch an STD ANY TIME you have sex. There is no safe time to have sex and condoms should be worn at all times.
Yes mam :) The most common std that's going around is HPV and you can have it without even knowing it. Symptoms can lie dormant for a long time and then can appear out of nowhere. It's always a good idea to use protection and get tested at least once a year.
It's always possible to get an STD while having sex, especially if it's unprotected sex. Even if it is protected though a condom, it's always a possibility. So yes.