No, PAN Card of Proprietor/Owner is consider as Proprietorship Business PAN Number. NO Separate PAN Card is Required.

Yes, You Can Start Multiple Business with Different Trade Name in Different Proprietorship of Single Person. There is no restriction on number of proprietorship registration.

All the License and Registration as per need can be obtain by Proprietor.

GST Registration – If Turnover is cross the Rs. 20 Lacs Limit

TDS Registration – If Firm Required Audit as per Income Tax.

PF Registration – If Proprietor ship firm have more than 20 Employees.

ESIC Registration – If Organization have more than 10 Employees.

Import Export Code/License – If Proprietor Wants to do Import Export Business.

Professional Tax Registration – Mandatory for Each Business

Shop Establishment (Gumasta) – Mandatory for Each Business

Food License (FSSAI) – If Proprietor Firm Engaged in food business.

SEBI License – For Brokerage Firm, Advisor Etc.

Depends on Banks Internal Policy. Mostly, documents are 

1. Photo of Proprietor
2. Business Seal
3. PAN Card of Proprietor
4. Any Government Registration Proof of Business (if Any Like GST, MSME, TAN, etc)
5. if Government proof is Not Available, CA Certificate of Business may be used in some banks.