Learn Russian: Я хочу приоткрыть окно, потому что здесь жарко. - I want to open the window slightly, because it is hot here.

In this context, при- acts as an attenuative prefix, meaning it scales down the intensity or completeness of the action. While открыть means to open fully, приоткрыть means to "open slightly" or "crack open."

Why is the perfective infinitive приоткрыть used here instead of the imperfective приоткрывать?

After хочу (I want), you use the perfective aspect for a single, specific action you want to complete. Even though the prefix при- means the window will only be partially opened, the act of doing it is still a single, one-time event with a clear result.

Can I use this same prefix to mean "to close slightly"?

Yes, you can use прикрыть to mean "to close slightly." The prefix при- frequently expresses this idea of an incomplete or slight action across many verbs, such as присесть (to sit down for a short time) or приболеть (to get slightly sick).

Why do we use the adverb-like form жарко instead of a regular adjective here?

жарко is used here as an impersonal state word to describe the general environment. Russian uses these neuter short forms to describe weather, temperature, or physical states when there is no grammatical subject doing the action.