1. Yes, you should be able to log back in as DRK in ULDAH on your ARR PC account. You just won't be able to enter any Heavensward areas which likely will include NPC's and zones your DRK would need to access for job quests etc. But since you unlocked the job and are in fact, standing in an ARR related zone...and since our characters must have a weapon equipped at all times, and since you can actually play as a DRK in old ARR zones, you will be able to access any pre-3.0 content on DRK on your PC ARR account.
2. No, you will not be able to FLY it in ARR zones (regardless of which platform/account you log into btw) as the only zones slated to allow FLYING are the Heavensward zones. Still, you will have the mount in your inventory...and if you can use them w/o flying them, then you likely will be able to ride it (but not fly it) in ARR zones. Although, it is also likely that the flying mounts will be 'greyed out' when you are in ARR zones and only usable when in zones/areas which permit flying (ala Heavensward). Although outside of SE saying 'flying mounts will only fly in the new zones', we don't know much about how these mounts will work/if they will work in ARR zones (again with or without being on a Heavensward acct).
3. Duty Roulette: This is a toughy but I'm thinking it's going to require you to be on your Heavensward account to do *if* you have a heavensward account. Meaning Once you unlock the content and it is in your Duty Roulette, you will only have access to your Duty Roulettes if on a compatible account. If however, you NEVER use/aquire a heavensward acct, then likely you will still have access to the 'pre 3.0 Duty Roulettes' only. Also, SE might make it so all pre 3.0 content is in it's own seperate Roulettes, so the only Roulettes you would not have access to if not playing on your Heavensward acct are the ones tied to 3.0+. ...or they might do a mix of these options. (Again, 3.0 Daily Roulette's haven't really been explained yet...but since level cap raises in 3.0, it is likely that 3.0 roulettes overall do not get mixed in with ARR roulettes...at least not all of them).
So in the Roulette world what is likely to happen:
If you have Heavensward on your PS4 and not your PC, and are currently playing on your PC:
You'll likely have access to these Duty Roulettes:
1. Low-level
2. Level 50 dungeons (once you unlock them)
3. Levequests
Why? because these are likely to ONLY contain pre-3.0 content and therefore would share no baring on Heavensward. Basically like how it works now where your low-level DR is unlocked and accessible as you level, but your Primal Roulette doesn't unlock until you finish the story/do said primals once.
And potentially might have access to
1. Primal Roulette (50 capped) -This is IF they cap the current primal roulette and start a new one +50.
Likely won't have access to:
1. Expert Roulette (these dungeons will likely be 'new' and level 50+ and therefore, not ARR content)
2. Frontlines
3. Any Heavensward-tied/tiered content. (So if even 1 dungeon/duty in the mix is from heavensward you won't have access....A la Hildebrand quests fing up your Primal Queues in this version)
What I'm basing my answers on: Recent SE interviews and dev statements/ how the gameplay works.