When China says they're not interested in full, overseas military adventurism, I actually believe them. China is so big, unwieldy and diverse that even in good times it's hard to keep it stable internally, and one thing the Chinese government is VERY good at is taking an EXTREMELY long-term view of its actions. If China decides to act against the US, it will be in myriad subtle and indirect ways that accomplish its goals without sudden shock and exposure.

Incidentally, the US itself is also a fantastic example of why China WON'T do that. Post WW2, with very few exceptions, almost EVERY instance of US military adventurism has ended in failure, or at the very least, not gained the US anything compared to the losses. But the US's work in soft power, partnerships, and containment? That brought down the Soviet Union without firing a single shot.

China won't be stupid enough to try to take America's place by using the US's loser tactics - it will do it using their successful ones.

I don't think China would team up with the EU explicitly, it would be more of a pact against a common adversary.