"La" is a determinant for femenine singular, so you can use it for speak of a especific sustantive who you know. For example, " La prima de mi novio" but if you don't know who is the cousin of your boyfriends you talk, you shall use "una", "Una prima de mi novio". In other hand, there is a mistake in your sentences, you shall say " se llama" or "es llamada".

Many moods of subjunctive aren't used usually, these moods are written in old books but we don't use for to speak. Subjunctive express probability.

It's more common not use the preposition "en".

Yo estaría dispuesta a hacer intercambio de idioma. Soy de Espaňa.