Hello Bentonj002 and welcome to DV!

By definition a lucid dream is one in which you are aware, i.e. you know you are dreaming.

It is in some of these moments that I have had dreams that I felt like I was half asleep. I could control what I wanted to happen. I just always assumed I wasn't actually dreaming, but that I was just having normal thoughts while I was half asleep. Would this be considered a DEILD?
It would be a lucid dream if you knew you were dreaming. In such dreams you can change the contents of the dream, what we usually refer to as dream control. Yet, you can also have dream control like for example telekinesis or flying without knowing you are dreaming. In such a case, those can be used as dream signs to help you achieve lucidity. That is, you recognize that a particular situation applies to dreams and become lucid as a result. DEILD is a lucid dream that is induced by falling asleep right after waking up from sleep. (Dream exit induced lucid dream)

I was asleep in my bed and I "woke up", except that I wasn't actually awake. I remember seeing one of my friends in my room and when I asked them why they were there they didn't reply. I kept asking them that and remember sitting up (in the dream, not actually. I think anyway) and eventually yelling at them
This is referred to as a false awakening. Although one is not lucid by default in such situations, one can train to recognize them and turn them into lds. DILD is when you become aware during the dream.

I hope this clears things a bit! You can read more about different ways to induce lucid dreams here:

Induction Methods and Techniques