So, to your first question: The pocket dimension will be unique to your familiar.
While it's difficult to prove this, a dimension that potentially contains the familiars of every spellcaster with the Find Familiar spell in the entire universe at the same time really doesn't sound like a "pocket" dimension.
Also, what would happen if a Wizard sent his familiar to the pocket dimension at the same time as the vastly more powerful familiar of his Warlock nemesis? You have to assume that the Wizard probably wouldn't ever see his familiar again, if you see what I mean.
To your second question: RAW, the familiar probably can't take items with it.
The spell says you dismiss your familiar, not your familiar and everything they're carrying. Similarly, "it" disappears into a pocket dimension - "it" here definitely refers to your familiar, there's no reason why it would mean "your familiar and everything it is holding". It's also worth mentioning that your familiar is defined as a spirit that takes the form of an animal - so maybe it could take spirit objects with it, but probably not physical ones.
Additionally, when asked a similar question for Find Steed, Crawford said that the steed should leave gear behind. While Find Steed is different to Find Familiar, its wording with respect to this issue is similar, so the same rules probably apply.
On the other hand, Mearls says he'd allow it, but only for a few minutes. The usual caveat applies here, of course: Mearls is not a source of official rules interpretation, just a source of how he would rule things in his game. So you can pretty much take or leave his advice as you choose.