"Homecooked" is typically written as one word.
"Lifetime" is one word.
mobile home
Homework is one word.
hometown is usually one word
"Homebuilder" is typically written as one word.
"Homework" is typically written as one word.
In internet usage, homepage is one word.
Lifestyle, life style, or life-style. All can be used.
one
Mobile home, two words.
"Home sale" is typically written as two separate words.