SATA specs requires the power lines/connectors to support 1.5 A per pin. So you are safe. You're only halfway with your new drive.
On a more general note, SATA is a standard. A HDD producer would not be allowed to sell the drive if it would function outside the standard.
You worrying about this issue is a bit funny, no offense intended
Supported capacities: all lower capacities are supported, this is just marketing b*&^&*hit. That's not the case with higher capacities, that's where you have to obey the specs.
7mm vs 9 mm drive size: the screw holes are also standard, so when you screw the drive onto the tray it will stay in the standard position, with a gap of 2mm above or bellow. Again, it's about standards here, the 2.5" drive form factor is standardized.