How can I see that its correctly patched?

The title screen doesn't seemingly change after i extract the patch inside the game folder. :-(

Change the game temporarily to windowed. You see it at the window title.

Is the patch supposed to remove the pixelation in the Rain scene in Anan trap pool? Because it did not do it for me.

No it's still a game with mosaic censorship by japanese standarts.
There is no uncensored version as it never was uncensored. You get the cut adult content back into the game.