"house"
In common English a house is a building where people live, but In England they also have the "House of Commons" and the "House of Lords". These are buildings where the elected members of government do their work. I don't know which meaning applies to your sentence. Maybe the Prime Minister led the President to his home, or maybe he led him to a government building (if it were a government building it would probably have a capital "H", ie: House)
"Molly had fought and overcame her fear of flying." (you write 'overcome' but it should be 'overcame')
Fought is the past participle of fight. If you are afraid of something you will have to fight against your fear. Molly fought against her fear of flying, and she won the fight because the sentence says she "overcame" her fear. To overcome something means to 'succeed' against that thing. "I overcame the mountain" means I succeeded in climbing it, for example.
"His threats become more intense, agitated, and frequent."
A threat is a statement about wanting to cause pain, injury or damage against someone. "I'll burn your house down!" is a threat, for example. A threat can be mild or severe.
Mild threats...
"I'll hide your car keys if you don't stop annoying me"
"I'll tell your mother that you smoke cigarettes if you don't let me borrow your car tonight"
Severe threats...
"I'll kill your dog if he doesn't stop barking at night"
"I'll break your legs if you don't pay me the money you owe"
"more intense, agitated, and frequent."
-intense means his threats were becoming more severe
-agitated means he appeared more nervous and angry while making threats
-frequent means the threats were happening more often