To be honest, it sounds like you need a welcoming FC that goes along at your pace, or is populated with people that share your type of play style. When you choose to use the Duty Finder, you will be paired up with God knows who - and this is the chance you take.
As someone else had mentioned, if you wanted this kind of experience, you should have started playing when the game initially launched. This is not a stab at you or telling you that you are wrong for starting to play when you did, but this is simply to say that most players would be new at this stage, and people wouldn't be rushing as fast as they do now (obviously). Also as someone else pointed out: MMOs can be kinda top heavy after a period of time. A lot of this game requires you to grind. Grinding for points, items, what have you. Players that are farming soldiery points for example, wouldn't really enjoy taking and hour or an hour and a half to finish a dungeon. Its simply not time efficient for their goal. Consider this, everyone you pair up with in DF may have a different reason for being in that instance than you. Does it make what they are doing, (rushing) while you want to enjoy the story - right? Possibly not, but you also have the option to leave the dungeon or make a preformed party to go at your own pace if you wish. You simply cannot force 7 other people to play as you expect them to.
Someone had also suggested getting or using a keyboard for the PS4 - I would totally second this. Communication is key in any MMO, and as you continue to progress through content, it will be increasing important to you getting stuff done.
ALSO, not all veteran players speed run or rush through everything. I had 3 separate Wanderer's Palace runs today where there was 1 or more people new in my party, in each run. Hell, the last run - all 3 people in the party were new. The discrepancy between our item level was pretty great to say the least (I was healing as WHM) and I had more HP than the tank (or both of the DPS combined). While I knew that this run could take a while, I didn't mind explaining things to the new people I played with today. Am I grinding for my relic items? Yes I am. Have I done 23 runs of WP with no drop? Yes. Would I prefer a 12 minute run? Absolutely. Do I expect this everytime? Of course not.