Hello there Sir! If your looking for a Fleet to join I would have to suggest you check out Aurora. We endeavour in all STO has to offer and do RP on our forums. You can find a link to our site in my signature. Good luck and warp speed!
You may find our fleet to be a good match for you. The biggest thing I noticed was the time difference. I'm in EST so it was easy to see that my mornings are your evenings almost exactly. And then you mentioned you play in the mornings, meaning you'd be on around evening my time which would place you in the peak time of our fleet.
About the Dilithium Sentinels - We're a smaller sized, tight-knit group of players and looking to stay that way. We're all about helping each other out in whichever ways we can, and moreover just having fun in Star Trek Online for all it has to offer us.
From what I've seen, we've got a few people that really enjoy PvP, but I'd say the majority are PvE'ers just trying to level up at the moment and team up for things. As far as RP, I will tell you that only myself and a couple of others have done the slightest bit of roleplaying, so if you are really looking for a place to roleplay, we probably aren't right for you. It just depends on how big of a factor some of those bullets in your list are.
Still, if this sounds intriguing to you, I'd invite you to stop by our fleet site at http://dsentinels.guildlaunch.com and check it out. You can also find me in game at @TheBigS412 if you have any questions or want to talk more.
I know how you feel about roleplaying. I myself have only watched a few episodes with my mom when I was little, and never really go into it. Then my friend showed me this game, and asked me to help him run his fleet. I've been RP'ing with him for over three years on a forum based RPG (Star Wars, of course :p) and because of his deployment with the military, I've taken his spot as leader.
If you are interested in the fleet (and don't worry about your rp experience. Everyone helps out in the fleet) friend me and then contact me in game. My main is Rorako@Rorako.