All of the appliances you mentioned are available either online (new and or used) or from exiting expats.
taobao.com (china's equivalent of amazon). As the site's in English only - you'll need to use machine translation software to dig around blindly until you figure out the correct Chinese phrase for what you seek. You'll need a Chinese bank account AND it has to be enabled for web access.
You'll also need to signup with alipay.com (chinese version). For the ID card - use your passport, but add LEADING (in front of) zeroes to pad the passport number so it totals the 18 digits common for Chinese ID cards (which you can't get).
And finally - you'll need a local mobile phone - all require your passport for registration. If they people helping you can't seem to get it done - remember the leading zeroes trick...
For the foodstuff(s) - any of the major farmer's markets (aka wet markets) around where you live will carry everything you need except the milk. You'll need to go to the milk store for that.
I'm lactose intolerant - but I have NO SERIOUS PROBLEMS with the New Zealand imported and packaged whole cream milk (1 liter per container), which we buy by the case (actually, 2 cases per month) - although there was that botulism scare a few years back...
You can also checkout jd.com and or tmall.com for the more genuine appliances.
We also have a couple of metro wholesale warehouses (german company). As a foreigner, just show your passport and they'll give you a membership card. For the Metro addresses, check the listings page on this website.
If your chinese is pretty good - you can also shop metro online (metro.com.cn?), but their prices actually not so competitive - so metro is best for picking up non-perishables (e.g. cereals, snacks, supplies, etc), frozen goods in bulk (like ice cream!), beverages, and imported goods...until you figure out how to make homemade Lea & Perrins sauce actually taste like Lea & Perrin's Worstershire sauce (as opposed to pipe cleaner and roach poison).
Best wishes with your upcoming visit. Kunming's a fun city and the entire province is a tourist bonanza, not to mention side trips down to the golden triangle (Laos, Cambodia, Vietnam, Thailand, Malaysia - and you can even jet over to Bangladesh, India, Pakistan, the many new and emerging <insert prefix>-istan middle eastern nations, etc if you're more intrepid). Just make sure you pay attention to and stay current with the US Consulate/Embassy Travel Alerts.