Not sure for a standard line but the record is "1100 kV voltage, a 3,000 km (1,900 mi) length and 12 GW of power". So presumably 11,000 amps or so for that one. I guess you can have as much current as you want by making the cable thicker.

Being built in China here approx https://www.google.co.uk/maps/dir/Guquan,+Putuo,+Zhoushan,+C...

It's quite an impressive looking thing (vid) https://www.youtube.com/watch?v=VZ2KfrP_R3s

so transporting 1 TW would be a hundred of those in parallel

Yeah, but the average EU power consumption today is 0.35 TW, so with only a hundred of those in parallel (more likely spread around the Europe) you could literally satisfy 100% of EU power demand, and still have plenty of spare capacity.

I guess something like that. Probably beefier pylons and more cable on them.

could submarine power cables in the Medeterranian sea be thinner since the water keeps the cable cool?

Dunno - bit beyond me that one.