I was born hard of hearing, not deaf as such...so I'm not entirely sure I'm qualified to answer this, but I can try. I'm not wearing my hearing aids right now, and if someone phoned me I would be able to hold a conversation, but would probably ask them to repeat things a fair few times.
I think in both words and pictures. The first thing I think in the morning is 'What time is it? Do I have to do anything today?' (I'm not working at the moment). Then I'll usually imagine myself briefly doing the activities.
I wasn't going to answer to this thread, as I think it's aimed more at people with sign language as a first language, and I don't know any, but I had a brief recollection which might be interesting..my hair has been every colour under the sun, and for a while it was entirely bright pink, and I had a lip piercing. But when I first got them, I had my usual, non-pink hair and non-pierced lip in all my dreams..it never filtered through to my dreams.
I speak in my head to myself all the time- I'm doing it now, thinking what I'm about to type. I thought, though, that it would be a mix, at least for most hearing people- my head 'speaks' 'I gotta get up and feed the cat', but other times I will visualise something- a shop, maybe, if I have to go shopping, or something like that.