Although you can file a trademark yourself its easy to make mistakes. More self-filed applications fail than succeed. Common mistakes lead to rejection by the examiner on absolute grounds, or by oppositions due to similarity. Some mistakes wont be apparent until you try to enfore your trademark rights.
No, owning a domain name does not give you any trademark rights.
No, registering a company does not give any trademark rights.
No registering a trademark in one country or registry jurisdiction give rights in other places. Trademarks are territorial in nature, registration only secures rights according to the area covered by that registry.