Yes, its perfectly normal to go out with a girl and not be in a relationship. However, you may need to tell them something along the lines of "I know that you've never said anything about a relationship, but I just want you to know that I'm not interested in one" or make sure they know that this isn't a date. Some girls take the idea of just an average dinner and throw around the idea of it being a date without ever asking you. However, every girl is different; some of us are outright with how we see things and others just keep their thoughts to themselves. Don't wait until after the dinner or whatever it is to tell them that this wasn't a date, tell them beforehand.
Now, signs to be aware of. Some of us have a certain "look" that we give to people we are attracted to. Im unsure of how to explain it but most of the time it's easy to spot. Its up to you on if you want to go out with friends after that or to reassure them that its nothing more. This is going to sound ridiculous, but avoid compliments. Compliments may lead to them being confused and thinking that they have a chance to change your stance. It's 3 in the morning, so this is all I can think of in the moment