Playing a game as the Japanese from the 3000BC start and it is about 1200AD. I have Seoul, Tokyo, Sopporo and some other city on the Japanese mainland down southwest. I was wondering, if I should invade China or would that decrease stability too much? I know Japan did occupy China for a while in WW2, but is the game script time based as well regarding to stability?

Destroy china. Vassalized Qin and adopt viceroyalty civic. You should be fine.

playing as japan, stability is always a big issue. if you control most of china you are most likely to collapse some time.
Destroy china. Vassalized Qin and adopt viceroyalty civic. You should be fine. China will also collapse if you take only some of their cities -> no vassal to take.
If you go for the uhv the best way is to turtle on your mainland.

But I invaded China from north to south and raized their northern cities. They started the war because they attacked my base in Korea. I just retaliated.

you won't have any big stability hit if you just conquer Manchuria and a bit of Mongolia. That should be enough to overpower China, and have it eventually become a vassal.

My strategy was (I was playing viceroy so this can be impossible to do at monarch) to become good friends with all the european civs, don't declare war at Mongolia or China and when you can ask a city, just do it because all the european empires will vote yes. They don't like mongolia;) I have conquered allmost 6% of the map by just asking mongolian cities:)
If you want to win an UHV victory just stay on your continent and there won't be any problem. Just give Seoul a Great Artist (important, if Mongolia declares war, and they will, you can blitz some cities.) And defend your continent.

I can't just turtle on my island if I want to be first in score at 1500AD. Usually China collapses early but in this game they are really strong. In fact they are even very solid stability wise. Even though I've wonderspammed and am well ahead in tech China is far, far ahead in points. I decided I needed to increase my landmass so I thought I could invade China. However, last time that I did that I some cityies started falling away. Should I invade or would it be safer to colonise islands in the Pacific or even Australia maybe?

I can't just turtle on my island if I want to be first in score at 1500AD. Usually China collapses early but in this game they are really strong. In fact they are even very solid stability wise. Even though I've wonderspammed and am well ahead in tech China is far, far ahead in points. I decided I needed to increase my landmass so I thought I could invade China. However, last time that I did that I some cityies started falling away. Should I invade or would it be safer to colonise islands in the Pacific or even Australia maybe?

Invade China, burn their cities down.

Yep, burning a few strategic citeies to help a collapse along shouldn't be too hard. The other option is to wait for the Mongol's to try and kill them, can improve you relations at the same time via a mutual war (Plus I have found in my games, if the Chinese don't collapse on their own, the Mongols do it for them)..