Learn Spanish (Latin America): He vuelto y el gato ha manchado el sofá. - I have returned and the cat has stained the sofa.

Vuelto is the irregular past participle of volver (to return). While most "-er" verbs form their past participle by adding "-ido" (like comido), volver is a common exception that you just have to memorize.

Why do vuelto and manchado have different endings if they are both past participles in the same sentence?

Manchar (to stain) is a regular "-ar" verb, so it follows the normal rule of dropping the "-ar" and adding "-ado" to become manchado. Volver is irregular, so it gets a special "-to" ending to become vuelto. You'll see this irregular "-to" ending on a few other common verbs, like escrito (written) or roto (broken).

Why is it el sofá and not la sofá? Doesn't it end in "a"?

Yes, it ends in "a", but sofá is an exception to the normal gender rules! Just like el mapa (the map) or el problema (the problem), it is a masculine word that happens to end in "a", so it always takes the masculine "the": el.

Both he and ha translate to "have/has". Could I use tengo and tiene instead?