The recommended time is May to October. But I personally think July and August is too hot and there may be wind or even sand storm in early May, also late October become cold in the north west of China. Just some personal thinking~
About the visa, you can stay in China for 30 days on a tourist visa generally; If the estimated stay is longer than that, you need to make it clear in the application form and ask for the Visa Officer's approval when submit your application..