Jupiter's influence in Halley's comet's path is plausible. I don't know about a 4 year difference, though.
I'm not aware of reports in Europe in 690 AD about a comet; certainly not like Bayeux' tapestry in 1066.
The Chinese have been more observant of the heavens (because of the influence of astrology in their political life) and they can be trusted. However, if they write years later after the event and there's nothing known written at the time, it's to be considered with caution.
The Crab nebula being a star that exploded in 1054 witnessed with a precise date only in China is an interesting case. Europeans have witnessed something earlier in the year, without a precise date, but the Chinese have said it was july 4th 1054. However, this was reported in China, a century after the event.
Because of the very umpredictable nature of comets (except for a few, notably Halley's) and the scarcity of report at the time, I wouldn't bet on this info. But it's true Halley's comet seems the most regular and visible one.

Raoul