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There is no definite way to get a Tulpa, so, like with any other non-standard creature, getting one is a matter of the story the GM and players are making.
The reply to all your questions is "Ask your GM." If you are the GM, the answer: "Decide what works better in your game."
Diego is 100% right of course. I am going to add some thoughts mostly as a DM. As Diego says, a PC can't create a Tulpa the way they can, say, a Construct.
So this is really three questions, but each extra question only is relevant if the previous question's answer is "yes".
1: Could a character have a Tulpa of a Heavy Horse, which among other things, is a horse with the Advanced Template?
There is no problem having more than one template, so the creature can clearly exist.
As a GM I would have no problem letting a PC hire or befriend such a creature if I thought it would not unbalance the game, ie the PCs were high enough level the Tulpa would not dominate things.
If it turned out to be bad for play balance I could just have the Tulpa go away.
2: If yes, can a character have a Guardian Spirit Tulpa, applying the Guardian Spirit template first, then the Tulpa template, meaning the base creature for the Tulpa is a Guardian Spirit?
3: If yes, would they get to choose which spell level the "Guardian Spirit" is "conjured" by, assuming the Tulpa is intentionally created?
The RAW answer to question two is no, likewise question 3.
Guardian Spirit is already a powerful spell that allows you to conjure a creature as per the spell description.
Would I allow an invented spell that somehow allowed you to conjure a Tulpa over and over? Nope. There are lots of ways such a thing can prove thoroughly overpowered and I don't trust myself to think of them all. Sometimes Paizo's whole creative team can't do that, it's one of the reasons you get errata or things banned in PF society.