e-residency and using limited company solely for P2P

Interesting, I have played with this idea as well. But what would be your benefit from it instead of investing as an individual person?

I cannot say anything towards the credit licence, this is an important question though.

First, about the FSA registration. I believe this is the text of the relevant law (a draft but I think it's mostly unchanged). In it, §4(3) defines a crowdfunding company as offering solutions to "investors". So if your company only invests its own equity capital, it would appear to me it doesn't have "investors" and hence is outside the purview of the law. NB - this is just my understanding. Don't act on it before getting legal advice.

Second, is it prudent to invest through an Estonian company?

For someone from outside Europe, that would make good sense since most of the euro platforms only accept clients resident in the EU (plus Switzerland, Norway etc.).

For Europeans, Estonia's status as a tax haven of sorts makes the idea attractive. However, many European countries have laws to the effect that if the sole/main purpose of setting up the company is for tax avoidance (and you are actively managing it from your own country), you can be made personally liable to pay tax on the company's income even though it is a separate legal entity in a different country. That would negate the only real advantage of this idea and thus render the whole exercise pointless.

It might work out better if you start an Estonian company with a couple of buddies (so you're not the sole owner) and do some other local business, however small, in addition to P2P investing, but that goes well into the domain of necessitating expert advice.

In any case this part of tax law has not been harmonized between EU countries so the tax implications will ultimately depend on which one you are resident in.