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.
Yes.
The familiar can travel any distance from the caster. The rules only limit communication, not travel. Also, someone else recently asked this to Mike Mearls, and he confirmed that is what RAW and RAI say:
Does a familiar have a max distance it can be from it's master?
Those limits on communication are greatly expanded for Warlocks with the Pact of Chain boon and the Invocation Master of Chain -- where the familiar can be communicated with, and see through senses used, anywhere on the same plane of existence.
Best Answer
Anywhere
You seem to be operating under the assumption that the "dismissal" of the familiar is a command that it must be given. But the spell does not require the familiar to be communicated with to be dismissed. According to the PHB, p. 239:
This is the start of its own paragraph. There is no qualification given for distance, so it can be done at any distance. Contrast this with the qualified other abilities of the familiar, such as needing to be within 100' to cast a spell through it, or within 100' to communicate with it telepathically.
This has been confirmed by JC on Twitter.