I know you have to make a resource match when buying attachments just like allies. And I thought this was in the directions, but could not find it: the attachment also have to goes on someone from that same sphere, correct? Like Gimli cannot buy horn of Gondar and then put it on frodo right?

No. Horn of Gondor can go on any hero. You just need tactics resource to pay for it. Unless an attachment says "attach to a (insert resource type) hero" it can be played on a hero of any sphere. Some attachments say play on a character which means it can be attached to allies as well as heroes.

So self preservation could be paid for by denethors resource pool but put on Gimli? Gimli could acquire a song of kings and then later pay to put Dunedain warning on eowyn?

Yes and yes. Also, keep in mind that you can play attachments on heroes controlled by other players (e.g. Gimli pays one Tactics resource for Horn of Gondor, which you attach to another player's Eowyn.).

Thanks guys, appreciate the help! This will definitely help game playing with my boys!

The only limits are what it says on the cards - so, for example, A burning brand has to go on a lore CHARACTER - doesn't have to be a hero, but does have to be Lore.

Generally though, so long as you pay appropriately, most things go wherever, most common restriction is hero only.