1st: You may use the same account as your ps4. Or you can make a new one too. Its up to you. Just note that any data related to your account on your PS4 will sync with Vita if you chose to use the same account.

2nd: UK is part of Europe, therefore R2.

3rd: For the 2nd hand game catridge, you have to make sure the game you got is R1

Sorry for the confusion. Let me clarify the last one for easier understanding.

Let's say you got a R1 PSN account and you got R2 game catridge, you can still play the game without any problem [trophies and etc] and the game will still be listed under the games you played in your R1 PSN account.

The only problem is that when you try to get the DLC for that game through PSN Store, the Store will state you don't have that game due to the Store is R1 Store [based on your account] and the game is not detected by the Store due to its being a R2 game.

And if you play online with that game, you'll be connected to the R2 server instead of the R1. [Need clarification on this matter though]

1. I don't think patches are considered DLC. Most likely, patches are independent of the account region and is based on the game region. So, if your game is R2, you'll get R2 patch.

2. Vita memory cards are locked to your PSN account, one memory card can only have one account locked to it. But you can format the memory card and reassign a new account to it if you want to change accounts.
There's no region categories for memory cards and any PSN account can be assigned to it regardless region.

nope, PS Vita isn't like the previous PSP which has PAL and NTSC specifications.
so any region console will work regardless your account region.

I'm planning to buy PSVITA at Japan.

The seller told me to register under US account, is that true? I do not have PlayStation account so far.