I believe that all certificates (academic, police, etc.) now need to be authenticated through the Chinese Embassy in you home country. That was new this year.

The system is now more bureaucratic, and documents are also sent to Beijing, that is why the process takes so long. It is making it much harder for employers to employ people who are not already in China, because of the lead times.

Pu er tea comes in many forms. The disc/cakes are naturally fermented, over years, and the sky is the limit on price (50rmb - 10 000). You are more likely to be cheated buying this kind of tea. Pu er also comes in other forms where they have used an artificial fermentation process. This latter type comes in tea bags and even little balls. The reason why people buy the artificially fermented is that it is cheaper, more consistent and easier to use.
The cheapest place to buy tea is in the tea markets, but you have more chance to be cheated and they will upsell you on quality or quantity or both, and you will spend a lot more than you intended. Buying in a supermarket you have fixed prices, although it won’t be top quality. The independent tea shops, well some are honest others are not. There are also chains of tea shops (Tea Tea brand?) that are more expensive than the supermarkets but you won’t get ripped off.
As for your question, would the one sold in the supermarket be acceptable? It depends who you are giving it too. If it is to send home, then yes. If it is for a Chinese person who is not a regular tea drinker, maybe, but it needs to be the most expensive box on the shelf with the fanciest packaging (face culture). If it is for a Chinese tea drinker, personally I would not buy tea as I don’t know enough about what I am buying, and it can be several hundred rmb for a small amount of good tea. You might be better off buying Whisky or cigarettes, at least with whisky there is the ‘face’ value of having the bottle sitting on display in someone’s home, even if they don’t drink whiskey.

Your question about renting has been discussed extensively before. Without wishing to sound unfriendly, a search would help you.
An employer will not help you get a work visa for part time work. I also doubt the authorities would grant one for pt work. The process for new work visas takes 63 days and would also require you to leave mainland China again.

Here is one www.gokunming.com/[...]
Try Google searching for 'gokunming rent', go kunming work jobs' 'gokunming cost' 'gokunming cell phones'etc. for specific subjects.

Be prepared to pay 6 or even 12 months rent up front.
Bring warm clothes. The daily temperature range can vary 15 or more degrees C, and central heating is rare.

The best way to search this site seems to be using google. Just prefix any search with 'gokunming...'