Domain and trademark rights?

Question

Domain name market

If the name of the site in the ru-zone has long been used by someone - is it possible to registrate in another zone without consequences and work in parallel?
And is it possible to somehow check that this company has an already registered trademark with the same name as the site?
The question is that after the launch of the project they do not show that you use someone else's brand, and about the possibility of working in parallel with them, for example, morkovka.ru for them and morkovka.com for me.
Thanks to.

Answer 1

In Google, upon request, зарегистрирован ли товарный знакa bunch of services are issued for checking online, for example this one

Answer 2

A trademark is registered in a particular country.
That is, you can register a domain name with a registrar from another country. Ideally, also register a trademark in the country of the domain registrar;)

Answer 3

copy code from standard wordpress themes