>

Lots of outright no chance responses, and frankly I expect it to go that way. A few counterpoint, though none I expect would be enough to sway him; that said I'm not intimately knowledgeable on the overall dynamics, and dumb enough to know my gut could be wrong.
A few things that may be relevant (and most assume a Ukraine win, though the unfortunate possibility that it could be years and it is not assured what will happen with Russian "claimed" territories, though I think and hope they will stay with Ukraine where they belong, but I don't think it's necessarily a major factor here):
-ukraine will need to rebuild, China is heavily reliant on exports that will be needed, from appliances to cement to solar panels to vehicles to steel. Cement alone is interesting as China has significant excess capacity.
-russia is on the decline, Ukraine has already won the respect of the West. There will be money for rebuilding, which China will gladly take of Ukraine will spend it with them. China also wants money from the west and this could be an opportunity to curb the West's shying away (both accepting the talk and future help on the rebuild). Russian decline, likely financial issues, diminished workforces, and limited allies with significant producing capacitors in a variety of goods means that China will need to make up for less trade in some areas and Russian limited options mean a disgruntled Putin or other won't have much for alternatives. 
-if/when Russia loses, and/or Putin is replaced there will be repercussions. The blame will go to Putin and those who chose a war that "shouldn't have been started" so in hindsight the visit would not be viewed as badly as it appears now. Arguably there is evidence of such feelings already. Also, while China may not want Russia to lose there are still benefits to China (More powerful in the eastern sphere). And, while a long shot, if Putin is recognizing winning is unlikely or too costly (monetarily, politically, etc), China accepting could be good for him (an excuse to use, additional info/intelligence even if Putin hasn't seen the light). If China accepts it doesn't mean they will do anything to help, so this alone could be a path to the meet helping.
-xi has no skin in the game. He will do what is best for him and China. It makes sense to at least see what Ukraine thinks they have to offer.
Just to reiterate I expect the answer will be no. But that doesn't mean I have a clue, or that a no today couldn't turn into a yes later or at least help backchannel correspondence (including with Russia, which may inform xi of things that play a role in his decision; so even a no could benefit Ukraine by stirring up other things for Russia to focus on or dissenters to speculate about). That's my 2¢, which frankly may be worth less than rubles.
I can't see Xi stepping into Ukraine. >

what would happen if Xi goes to Kyiv to show his public support for Zelensky? >

That would be counter to what he has been doing: increasing support for Russia.  source >

then what would be the appropriate way for Xi to respond to Zelensky's invitation? >

Nothing. China is in that weird spot no matter what action they choose, it will do poorly.
1) If China support Russia--well, possible sanctions, possible nothing. West opinion of China will not improve.
2) If China support Ukraine-- No additional benefits, hostile Russia on their northern border, western opinion will not improve--and certainly wouldn't help get Taiwan back. if Russia collapses/fall into a western controlled puppet (Yeltsin II), it wouldn't help China either. 
So basically geopolitics dictate China to sit on the fence. No matter who wins in this war, it is unlikely they can cut China out from the future. 
So the answer is to do nothing. >

China also undermines their own geopolitical position if they support Russia too strongly. It tarnishes their legitimacy if they don't support territorial integrity and opens the door for more nations to support Taiwanese independence. >

Taiwan is always considered part of China from China point of view. In their eyes, you can support other countries territorial integrity and demand eventual reunification of Taiwan. 
But lets face it, it is not like China (and everybody else) took on Americans when they stormed Iraq or when Russians charged Georgia. Talk is cheap. 
Most of Taiwan's western allies will not change their mind of China-Taiwan issue, nor will China. Whatever happen in Ukraine is irrevlant. >

Yes that’s the point. 
Supporting Russia is saying territorial integrity is not important because they have invaded and annexed parts of a neighbor multiple times. China’s justification for its Taiwan policy is territorial integrity. 
You’re right that it won’t make a difference though. No one in East Asia really trusts China anyway aside from maybe Singapore, so no one expects them to have consistency in their policies. >

Singapore does not trust China. Singapore’s foreign policy is to trust no one. >

Ukraine about to join the Belt and Road Initiative >

They were already part of it, but the war derailed the ongoing investment project.
As a side note, it's very likely Ukraine will take advantage of Chinese help for reconstruction. They don't have to be tied solely to the West for what's going to be a long, costly rebuild of their country. >

Don’t forget that technology transfers from Ukraine — not Russia — formed the basis of many Chinese military equipment. >

Yes. The most striking example is probably the Liaoning, the first Chinese aircraft carrier that is in fact the rebuilt Ukrainian/ex-Soviet Varyag kutnezsov-class carrier (though bought under cover as a floating casino). >

Y'all gonna have an aneurysm when you find out Ukraine and China have good relations. >

Welcome to the black and white world of the Reddit hive mind. >

Who are you declaring yourself superior to in this comment? >

clearly the implication is the average redditor >

Vague response from Xinnie the Pooh about how much China cares about 'world peace' but respectfully declines to help facilitate it actively, incoming in 3,2,1... >

We are just now hearing that China is currently Bing Chilling on the situation. >

Good move.  Make him a global focal point. >

It’s probably just a posture. Putin is pretending he hope for peace, all while making demands that are unreasonable and blame it on Ukraine for not accepting it. To counter it, call them out and make their own counter-posture, like "You hope for peace, you say? We’re the one actually trying to get a just peace here," is a pretty book move.