1. He tattos a rose on his arm.
2. He woos the girl to marry him.
Are the sentences grammatical?
In the first sentence, the only error is spelling. The word should be "tattoos" -- double t.
In the second sentence, you don't need "to marry him." That's what wooing is -- to court a girl and get her to marry him. If you want that idea in there, though, you could write this: He woos the girl until she marries him.
=)