Hi @Prakhar and welcome to the community!
a) No, you don’t need any additional bank account.
b) You need at least a legal address and contact person, which often will cost you 300-500 EUR per year. The cheapest offer I’ve seen is from Nordic Consult, which charge 125 EUR per year.
In addition you need to do accounting for the company and submit an annual report. It’s possible to do both on your own, at least if you have some accounting background, but it’s not recommended. If you only have a few transactions per year, then it might not be so expensive to outsource. If you go over the VAT threshold it gets more complicated as you’ll have to submit monthly reports.
Finally, I’m not sure if you can open a TransferWise account if you don’t qualify personally. Normally you’ll open a personal TW account, and then from there open one for your business. Business accounts are always tied to your personal account. So before going ahead and opening an Estonian company, I’d recommend that you contact TransferWise to see if you would actually be able to open an account.