Hi! I've got some problems with interpretation of some house cards.

For example when gregor cleagne vs damphair, what is the number of swords that clegane gets fighting damphair when he switch card ? Is it when lannister is higher on the fiefdom track he gets 3 swords, and when he is lower he gets 3 minus the strenght of the card that damphair switch? Same with Tyrion, does he swtich opponents house card before any special abiliti or in fiefdom order, so the effect of special abiliti of the first card will take place ?

When it comes to Tyrion vs Clegane there's an answer on page seven of the official FAQs

"Q: When is the effect of the “Tyrion” House card resolved?
A: This card is resolved immediately after “cancel” abilities, but before other effects. "

Since Clegane has no "cancel" ability Tyrions effect has to be resolved first.

When it comes to Clegane vs Damphair I see no alternative to sticking to the fiefdom order as you did. Neither Clegane nor Damphair have a "cancel" ability so none of them gets priority.