Yes, you need to register your desired domain name at the domain name provider/registrars. As the principle „first come, first served“ applies in domain names registration, the rights to the certain domain will be held by the first person registering it.

Registration of the domain name is mostly simple process in which you do not have to proof any kind of authorisation to use selected domain name. If it is free of course. No authority examines whether domain name selected by you infringes any earlier intellectual property (IP) rights of third party. This is the reason why many speculators register existing trademarks as domain name and then try to force holder of the trademark into buying this domain from him. This is however illegal.

You have right to use your domain, attach content to it, publish content on it, transfer domain name or license it to someone else.

Your rights to your domain generaly lasts as long as you are the owner of it. Basically once you stop paying for renewal of your domain name, you stop to enjoy rights to it.

Yes, the trademark is different type of IP protection and thus can be used to protect your domain name and streghten your position. You can also trademark only a part of domain name. For instance if you have a domain name „klabadooo.com“ you can register only „klabadooo“ leaving „.com“ part behind.

In fact most businesses trademark their domain names in order to get more efficient way to protect their rights to it.