Thank you for your questions.
Yes it is possible to get sexually transmitted infections such as Genital Herpes or Human Papilloma Virus even after protected sex. The infection could be passed on through blisters or warts in pubic areas which remain exposed even when using condom.
The Bartholin gland function is to secrete mucus to lubricate the vagina. It could therefore result in the formation of a cyst, if the gland gets infected by STDs or other infections due to the gland ducts being blocked and unable to release the secretion.