I'll preface this by saying I don't live in Japan but am pretty confident this is all true. If anyone knows better though please feel free to correct any mistakes
With HDMI now you shouldn't have any problems connecting any of your consoles to a Japanese TV.
You shouldn't need step-up converters for newer consoles either. The old style (fat) PS3 was fine at any voltage and I presume it's the same for the slim and super slim. Most consoles with a power brick should also be fine, you can check the brick itself as it'll have a sticker on it with details about voltage etc. if it says 100-240v then you're fine. I've been using my UK 3DS charger in Japan and it works fine (and also works on my Japanese 3DS LL).
The lower voltage doesn't mean slower charging, lower voltage just means it takes more current to amass the same amount of power in watts (P=VxI).
You shouldn't have any problem accessing your UK accounts in Japan but certain services (iPlayer at least) will be blocked. To access the Japanese store you would need to make a new account with a new PSN ID. That should be pretty straightforward on the PS3, not sure how the Vita handles multiple accounts but you could always download Japanese Vita games on the PS3 and transfer them via USB to the Vita.
With the PS3, you could buy one in Japan and access your UK account which might be easier plus has the added bonus of being Region A for Blu-Ray (UK is region B) in case you wanted to buy any here. Loads of Blu-ray films don't bother with region coding but some still do so worth thinking about.
I'm not 100% sure about the 360, I remember getting a JPN account on my UK Xbox and it didn't last long before I couldn't access it so I'm not sure if there are any restrictions there. 360 is not much loved in Japan so buying one may bring shame on your family...
Edit: it's also easy to buy chargers for handhelds in Japan and I'm pretty sure I've even seen Wii U power bricks (official) for sale so you could always get Japanese plugs to save using adapters.