Remove Hello There, Guest!

[Erik24]

How can I edit the Hello There, Guest! from top section by log in buttons?

[Destroy666]

Edit the header_welcomeblock_guest template. You can remove {$lang->welcome_guest} from it.

[Erik24]

Edit the header_welcomeblock_guest template. You can remove {$lang->welcome_guest} from it.

Can I also just add my own text to replace it?

[Destroy666]

Yes. Either add it to the mentioned template or edit the language string:
inc/languages/[your_lang]/global.lang.php -> $l['welcome_guest'] = "Hello There, Guest!";