Sushi rice not sticking to each other
It's hard to say exactly which thing was the issue. Rice sticks to itself because of starch on the surface.

As Joe pointed out, if it's actually still wet, it's not going to stick. It doesn't get sticky until it's dry enough for the starch to be sticky instead of just starchy water.

But even if you did let it cook/dry properly, the extra washing and soaking could well have been an issue too. One of the main things washing does is remove starch. If you manage to remove too much, you could well stop the rice from being sticky.

So... I'd suggest following the instructions that came with the rice, and seeing how it goes. It might be suggesting less washing and soaking than you expect because it's a less starchy variety of rice.