The verb "to have" conjugates as:
Singular
- I have
- You have
- He/She/It has
Sarah is neither First (I) or Second (You) person. Sarah is third person. So the sentence is
Sarah has a red car.
So my original answer was incorrect. "Hope this helps!" is a declarative, not an imperative. Instead of deleting my answer, I think it might be helpful to explain why I should have known it wasn't an imperative, and pull out the bits from the original that were correct.
Imperative clauses are usually in the second person, like:
"Hope for the best!" (You should hope for the best.)
A declarative clause is just a statement, like:
"I am editing my answer." or,
"Hope this helps!"
The second person and first person form of hope are the same, so I got a little confused because I didn't think about it carefully. I should have been able to tell that the clause wasn't an imperative because an imperative is usually a command directed at another person, and "Hope this helps!" is stating something in the first person.
I would expand "Hope this helps!" this way:
I hope this (answer) helps you.
You would say "This answer helps me." and not "This answer help me." because the subject of "help" is third person singular. So, "Hope this helps (you)!" is OK, but "Hope this help (you)!" has a verb agreement problem.
In your suggested sentence, which is grammatical, you changed the wish from the present (helps) to the future (will help). This is OK, but it's not exactly what the original author expressed.
Best Answer
The sentence could be read two ways.
One, which you may have intended, is that there are two things that help you save money: 1) living at home and 2) eating your mother's cooking instead of going out to eat or buying your own food.
Another way you could read it is that it is just one thing: "living at home", which has the added benefit of enjoying your mother's cooking. One reason a person might interpret it this way is that "enjoying" isn't really relevant to saving money.
If you wanted to make it clear you meant the first, your could rephrase it to make it clear you meant two different activities. Perhaps something like: