Wait. Are we talking about a setup with an Estonian PSP or without? With a PSP, the location of the parent does not matter much. Without, it does not make sense to process more than 1M as the savings on interchange rates are substantial beyond that.
Yes, if you are doing e-commerce (e.g. amazon) in Europe, you will need an EU entity for compliance reasons and also to save on the payment processing fees (I know you can solve it all differently, but I don't think it is worth it).
You already have Singapore? Are you paying tax? Which agent did you use for the nominee director?
I was planning to use Singapore for a business idea. However, the plan is currently on hold, so I do not have any practical experience yet.
Many nominee directors don't like non-resident companies, especially if you do not use their accounting services (their liability includes the nominee directors personal funds).
Accounting will be time-consuming or expensive -- if you have tax-free foreign-sourced income you can not use form C-S and have to use form C (e.g. financial statements and tax computations have to be submitted). Usually if your revenue is below 5M SGD form C-S (the shorter form) is sufficient.
Operating without access to local banking is also harder than you might imagine, many Fintechs use local licenses for their Singaporean customer (e.g. Airwallex, Wise). Getting liable information on operating as a non-resident company is quite challenging, even from local tax professionals and lawyers you will get contradictory opinions.
You can find solutions for everything, but it is not as easy as some people suggest, especially if you try to be a non-resident without taxes. The alternative could be to accept the taxes and minimize the profit by paying yourself an employee salary that is not taxed in Singapore (only director fees are subject to taxation in Singapore). Besides that there are quite a few more ways to minimize the taxation in Singapore, you won't end up with 0%, but significantly less than 17%.