You need to apply for a China Tourist visa(https://www.travelchinaguide.com/embassy/visa/tourist.htm) from Chinese embassy in India before leaving. From 16th March 2009, Indian Passport holders applying for first time Tourist Visa are required to submit Original Bank Certificate with minimum balance of Rs 1.5 lacs. The requirements are as follows:

1. Original passport which has more than 6 months left before it expires from the date of application for a visa and sufficient blank visa pages.
2. One completed Visa Application Form for P.R.China with a recently-taken passport photo; all the items on the application form should be completed neatly with genuine information; if the applicant has a Chinese name, the Chinese name should be filled in; false or incomplete information and illegible characters may lead to refusal of a visa.
3. Proof of sufficient finances to cover all expenditures in China when required.
4. Confirmed return flight ticket and its photocopy.
5. Covering letter from applicant's company or office.
6. Photocopy of personal data page of applicant's passport.

I didn't see any special Indian VEG hotels in Shanghai, but you can easily find Indian Food in Shanghai(https://www.travelchinaguide.com/cityguides/shanghai/dining/indian.htm) and Vegetarian restaurants in Shanghai(https://www.travelchinaguide.com/cityguides/shanghai/dining/vegetarian.htm) . For Budget Shanghai Hotel, you may try Manhattan Bund Business Hotel, Shanghai which is a 3-star hotel with a reasonable price.