Could the character uses the sword's Bless This House to increase the strength of a threshold and then leave the sword behind and have the effect persist? Obviously the character is choosing to make use of the sword in this way so they wouldn't get a compel on the sword's aspect because they have been denied its use.
I would say Yes (as they wont be getting it's other benifits) and because they may still be compelled related to the sword to have someone move it, take it, or otherwise void it's benifits.
If the character also has Bless This House would the two powers stack like they would if they were on separate characters?
I dont really see why the character would have it twice (paying for it twice seems kinda lame) so I dont really think this situation would ever arise, but if it somehow did, i would say Yes they would stack.
Holy Touch lists skills affected as "Many", but it only mentions the effect for the Fists skill. Would the sword do +1 stress when used with the Weapons skill? If so, would you also get the +1 stress when using Fists while the sword is sheathed?
I would say the +1 would Not stack as it doesnt say anything about it stacking. I would allow your fists to be a weapon one with the swords abilites but you would have to have it on your person, and for me personally, as a gm, i would require it to be unsheathed, but thats just me.
Would Holy Touch's compel effect work when touching a creature with your hand or would you have to touch it with the sword?
I would say, as long as the sword is "active" (which for me would be having the sword unsheathed) it would work, even if you dont touch them specifically with the sword.
And finally, I find this bit really vague, "This could qualify your touch as satisfying a Catch for the Toughness powers of some creatures." How are other people interpreting this? Does it satisfy all "Holly Stuff" type catches?
I would say it satisfies all "Holy Stuff" type catches and possibly other if it fits, though the others part is up to you/your gm.