Question-wise answers to you are as follows:
Do we have to deduct PT for our employees?
Yes, even if you employ a single person, you are liable to deduct PT as per the slab every month and remit it either yearly or monthly, depending on your last year's liability.
Do we have to pay PT for the company as an entity and on behalf of employees?
If your company is Private Limited, Limited, or LLP (from 2018-19 onwards), you have to pay PT in the name of the company under PTE. On behalf of employees, PT is remitted under PTRC.
Does the company need to get registered for PT, or the employee also?
The company needs to register and obtain PTRC, under which remittance of PT deducted from the employees' salaries is to be made. The company needs to enroll under its name in the case of Private Limited, Limited, or LLP (from 2018-19 onwards) and pay PT annually. Each owner, i.e., proprietor, Partner, Designated Partner, Director, should have their own PTEC and pay PT annually.
What is the process to register employees and the company for PT in Mumbai, Maharashtra?
The process is online and tedious. If you are willing to get this work done, please contact my office at [Phone Number Removed For Privacy-Reasons]. My office will assist you in completing it for appropriate charges.