Learn Russian: Ты любишь чинить краны сам?

Сам is an emphatic pronoun meaning 'by yourself' or 'personally'. It highlights that the person does the action without help. Себя is a reflexive pronoun meaning 'oneself' as the object of an action (like 'I see myself'). Since you are fixing the faucets, not fixing yourself, you need the emphatic сам.

The sentence uses сам, which is masculine. What if I am asking a woman?

You would change it to the feminine form: Ты любишь чинить краны сама? The pronoun сам always agrees in gender, number, and case with the noun or pronoun it emphasizes (in this case, ты). If you are asking a woman, you must use сама.

Could сам be placed right after ты instead of at the end?

Yes, you could say Ты сам любишь чинить краны? Russian word order is flexible, and words placed at the end of a sentence often carry the main focus. Putting сам at the very end strongly highlights the 'by yourself' part of your question.

Why does краны look like a subject (nominative case) if it's the object being fixed?

It is actually in the accusative case because it is the direct object of чинить (to repair). For inanimate masculine nouns like кран (faucet), the accusative plural is identical to the nominative plural (краны).