1. She's never done that without outside help, and I'm not sure how you're using manipulating because all they do is move it. They don't change it or anything of the sort. And how is moving the Sun going to equate to her avoiding his attacks, which are also FTL since they outpace his flight speed in space. Also SpaceGodzilla has gravity manipulation "Using countless crystals formed on Earth and taking in an endless amount of energy from space, SpaceGodzilla attacked Godzilla by creating a combat field that allowed it to manipulate
gravitons and electromagnetic radiation as it pleased" referring to their movie fight and his city sized crystal battlefield so your stance is flawed.
2. Uh...they'd be so much faster it's ridiculous. He can manipulate gravity, which is proven to dilate time and even the speed of light (black holes are the best example of this). He's also been shown flying FTL in space and as previously stated he could easily take the fight to the stars.
3. SpaceGodzilla's mental prowess FAR exceeds Godzilla's since he has such things as telekinesis which can direct objects from interstellar distances and Godzilla's shown direct resistance to mind manipulation, several times in the Heisei series which would then apply to his clone, and Mothra who also has mental powers didn't even dare face SpaceGodzilla.
4. Can't mind rape him and she's both slower and weaker so nothing really proves she'd say bypass his energy forcefield.
5. He did. I quote from the accepted game origin "A mutated organism created from Godzilla's DNA that had been scattered in outer space during a fight with a rival, which subsequently crystallized and synthesized
inside a black hole before absorbing the energy of a fixed star. Highly intelligent, it invaded Earth in order to kill the original Godzilla." In the game version, a white hole is never mentioned. So SpaceGodzilla only had a few options of escape-flying faster than light or overpowering the gravity of the black hole. Either way, you can't tell me he didn't when the game states it as fact that he DID. Also wormholes weren't really mentioned.
Here's my source
http://static.comicvine.com/uploads/original/14/147508/5030479-space+godzilla+(2).png