By running instances and doing the instance quests, do you get the equipment you need to keep up with game content? I am especially thinking about Cata dungeons. I read that the dungeons there are brutal if you are under-geared and that getting the quest greens will help a lot more than having WotLK blues/epics.

Finally once you hit level 85 by doing the dugeon runs ( assume doing Utgarde Pinacle as Candlebox wrote) do you have the ilevel to start doing 10m and 25m LFR?
Yes you get the gear you need from instances assuming you have BoA's, if you dont have BoA's then you will still get the gear but one or two toons may fall behind for a couple instances.

Cata has ilvl requirements you wont be able to reach until about halfway through hyjal/vash.

LFR has a minimum ilvl as well but when you reach 85 you can buy enough crafted/boe gear to get in.