I have 6 characters I " actively " play this week, I collected all of the weeklies on my main and did the entire questline on him for K’aresh.
I now have the cloak to 707 with all characters, but I can’t see the weeklies on 4 of 5 of my alts, and on that 5th one I only see the Worldsoul weekly, not the Delves one.
Just odd I guess, missing Sparks because it’s been this way the entire week
These quests may already have been completed and are not necessarily weekly, rather on a rotation every few weeks.
For instance, this gal could only complete the 100 disc fragment one this week. I had already done the Worldsoul and 3x Delves ones last week.
On a side note, the old actual zone weeklies (Theatre, Key flames etc…) that had keys and such still work if you want Delve keys, though they only give half a key (50 shards) now.
I still managed to get my 2 sparks somehow, sadly I don’t remember which activities awarded them.
Did you do the phase diving one where you fill the bar up doing phase diving things, then turn it in to the guy next to the one you get your cloak from? That awarded a fractured spark. (eta - now I am doubting myself. It was either that weekly OR the Special Assignment out in K’aresh that gave a fractured spark.)
There should be at least two weeklies available in Dornogal each week.
There is! Arena may as well not exist though. 
(For me anyway)
They reset and when they do they are the same quests all your alts get … and they are not showing up.