Does " a roof over their head when they come home" mean "(worrying) the question of their house"?

no one who fights for this country ever has to fight for a job or a roof over their head when they come home. (Cheers, applause.)

to fight
for / job or roof over their head.

fight to (worry about) getting a job or making sure they have a home

Thank you.

By the way, what does "ph" mean in the context below?

America, I believe we can build on the progress we've made and continue to fight for new jobs and new opportunities and new security for the middle class. I believe we can keep the promise of our founding, the idea that if you're willing to work hard, it doesn't matter who you are or where you come from or what you look like or where you love (ph). It doesn't matter whether you're black or white or Hispanic or Asian or Native American or young or old or rich or poor, abled, disabled, gay or straight. (Cheers, applause.) You can make it here in America if you're willing to try.

It means "phonic" meaning the transcriber spelled something the way the heard it (as opposed to knowing they got it 100% right.)

It was most likely "who you love" and the transcriber heard "where."

He heard Obama read love as /lʌf/, not /lʌv/?

Good catch.