I think our relationship is great!

They live in their world and I live in mine, sometimes they even make the extraordinary effort of giving me a smile, the despising sights are more common but I feel contented if they just don’t spit in the floor, we occasionally share the same air and the same sun...

What more could I ask for?

Don't mix business with pleasure. I keep my private life private. I turn up to work, do my job well, and then go home. I'm courteous and I mind my own business. This has seemed to work well so far

Answers to your 2nd and 3rd question: no and no.

my relationship with my Chinese colleagues is purely professional and courteous.

I am in contact with them if it is required for my work, other than that, no.

work is work, private life is private life. 

mixing them is not a good idea

I go to the same Chinese fast food place for lunch every day. A bunch of my Chinese colleagues also go there. Only one Chinese colleague eats with me, pretty much every day, and we have some good chats. All other Chinese colleagues seem to avoid us like the plague, or it might be just me being the only foreigner.

In my department we only have 4 Chinese to about 25 foreginers. These four guys are really nice, ehem "normal" people, I chat with them, joke with them eat lunch with them. The other departments which are dominated by Chinese it is quite different as most of those guys are much more traditional, shy, quiet and awkward and usually keep to themselves. 

I'm the only foreigner in my company.

* Seniors, did their PhD in USA and worked there for at least 15 years : we often eat together, nice informal talk on a weekly basis. About two time a year, we go out for a diner in a nice restaurant with the spouses/husbands and their kids. I know their kids personally, etc.

* The others, who never left China and are under 30, with 3 to 5 years of education in university. Most of them don't talk with me, but they will salute me with a shy smile. They never eat with me, unless I seat with them if I bring my lunch box. The only talk we had so far is about who cooked the content of my lunch box and what it is. For work, I sometime need to talk with some engineers. They will avoid as much as possible direct interaction, because they are scared to death to loose face (actually, their English is good enough for work). I managed to make one more relax now, but it took 2 months of... I don't dare to say it, but this is what it is : taming. I remember watching colleagues arguing 20 minutes who should go to talk to me in my office to ask a question. I'm a small guy, very quiet, very careful to not hurt feelings of anyone, I can speak some Mandarin, etc.

I have a few work colleagues who speak good enough English. In the office, we can be fairly chatty (normally only 2 of them and myself), with a couple of the others occasionally joining in. I don't normally do anything outside the office with any of them, though I have one of them on wechat, so the occasional message will get sent, and comment on a post.

Most of the rest of the staff stay in their little world, as I stay in mine.

it is pretty normal, we chat, sometimes i ask them to help me to buy things on taobao etc. But anyway i noticed one strange thing, sometimes one or two colleges i  don't know decide to talk to me and get my wechat, finally the next day they show no sight of knowing me, like we are strangers again.

The Chinese staff are great. They do all the jobs that I hate. If ever I need somebody to wipe the leaves on the pot plants or crawl under desks to plug a computer in, you can always rely on the Chinese.

Not many forigners in the place where I live and work. All my colleagues and vast amjority of friends are Chinese. Some of them can speak relatively good English, some not so good and some cannot at all. I do not have a trouble to interract with my colleagues and friends. We frequently go to eat together or to the KTV.
At the end of the day we are all human beings living and working in the same place and therefore having similar desires and problems.
Saying that however there is a big difference between us in identifying what is a problem and what is the best way to solve it. This part is sometimes a bit frustrating but it teaches me a lot about Chinese firends points of view and attitude. It also teaches me a lot of patients.
At the end of the day what's the reason to go to foreign country if one would not like to get exposed to local environment and to certain, possible, extent try to integrate.

All chinese staff in my training school. Most don't talk to me outside of work-talk, but when someone considers leaving the school for whatever reason, we connect. 1 on 1 talks are rare. But they usually leave soon after. One older teacher (my age) can be fascinated by my opinions, and will ask my advice on occasion. I have fun talks with her during 10 minute breaks between classes, where I even bring up stuff from ECC now and then. The rest are 21-24 yo, mostly girls. Not much to talk about. I rarely eat with them. They're not bad people, just different values, priorities and interests. The 'older' teacher recently commented that our age (32) is considered OLD. Like a lion will jump out of the bushes and eat me at 40 for not walking fast enough. Maybe this is why colleagues have trouble connecting with me; my interests are on securing education for my 2 sons and relaxing (alone) when I have the chance.

Relationship with Chinese colleagues...

I am the only male in my office.
I am the only foreigner.
I am the only one under 40.
I don't believe in 'small talk' So....

There is no relationship.

I was probably in a better position in my last job that I knew quite a few of my Chinese colleagues on email before coming here, so at least they knew my working style. 4 years of working closely in the factory & I could have reasonable chats with quite a few of them. We didn't socialise a lot outside work but I'd say I had works dinners at least monthly with some of them. Politics was generally avoided but we had some good chats about differences in culture, etc. I wouldn't class any of them as close friends but as colleagues they were great. Some of them even came to understand my sarcastic streak!