Learn Russian: Анна, ты сама установила эту новую розетку? - Anna, did you install this new socket yourself?

Сама is the feminine nominative form of сам (oneself). It modifies ты (you). Because the speaker is addressing a woman (Anna), ты acts as a feminine pronoun here, so the emphatic pronoun must match her gender and case.

Could сама be placed at the end of the sentence instead?

Yes, you could say ...установила эту новую розетку сама? Placing сама right after the pronoun (ты сама) emphasizes that "you yourself" did it, while putting it at the end focuses a bit more on how it was done ("by yourself" or "without help"). Both are perfectly natural.

Why are the words эту новую розетку in the accusative case?

They form the direct object of the verb установила (installed). The basic feminine phrase эта новая розетка changes its endings to -у and -ую because the socket is the thing receiving the action.

Why use the perfective verb установила rather than the imperfective устанавливала?

The speaker is asking about a successfully completed action with a current result—the socket is now in the wall. The perfective aspect (установила) focuses on that exact completion and result, whereas the imperfective would just ask if she spent time working on it.