Consider also that your partner may be motivated more or less exclusively by sexual motives and may therefore be willing to lie to you in order to get you into bed. Be smart, protect yourself and don't let yourself be rushed into anything for which you are not ready.
It's completely reasonable for you to assertively require the use of condoms and other means of protection from STDs and unwanted pregnancy.
The first and most important rule is that everybody has to be on the exact same page.
Intimacy involves vulnerability; you become more intimate and thus more trusting and open with a person by virtue of the fact that you make yourself vulnerable in front of them and you learn that they will not abuse you.
Emotional intimacy takes some time to develop, but these days, this is not necessarily the case for sexual intimacy.