Non-resident alien corporation tax liability
1. Will I be liable to the US for income earned by my company?
2. If so, is this at entity level or personal level?
From your description I would like to address a few immediate issues, and also answer your questions:
1. It is practically impossible to open a bank account without being physically present in the US. Many rumors that we heard and checked where companies would offer such service for a hefty fee turned out to be either fraud or questionable service with no guarantee for positive end result. This is unfortunate, but if you want to open a bank account in the US for your company it might just make sense to make the trip here. The good news is you can open the account in almost any state, regardless of the state of formation.
2. If you are not going to sell to US clients you don't need to worry about storing your merchandize in a state with sales tax. You are only liable to collect sales tax from clients in the state where you sell in retail and have established a nexus.
3. I don't see how your company will have any profit, provided it will only be used to purchase merchandize for further reselling in China. It might make sense to form a Chinese company that would be responsible for the actual sales in China, and then use the US company to buy merchandize in the US and then resell it to the Chinese company at cost. This way you maintain zero profit for the US company. You would still need to file tax returns every year, except this way no tax will be due.
To better understand and plan your taxes I would recommend you to talk to an accountant, specializing in international accounting.