When you walk into a house that you own there should be an owner's UI on... I think the right side of the screen. You need to go to that tab and write in the player's name (that you want to invite) EXACTLY as it is written and then click the "add guest" button or whatever. Hopefully that helps.
I hear you and singing kumbaya together sounds nice but we're rogues, Takumi isn't a united village like the others, if that's what you're looking for maybe Sand is for you... VRChat is pretty peaceful too!
Idk where the dog is but whoever told you that you need to find a dog to get your mastery is messing with you. You get your first mastery at lvl 10 and your second mastery at lvl 50. GLHF man.