Извините, можно войти?

Yes. Извините is the polite/plural imperative form of извинить (извините! = “Excuse me / Sorry”).

• Извини = informal (to one person you’re on ты terms with)
• Извините = formal (to one person on вы terms) or to multiple people

In this situation it’s best understood as “Excuse me”—a polite attention-getter before asking permission. It can also function as “Sorry,” but in Извините, можно войти? it’s typically “Excuse me…”

Можно means “it is allowed / it’s possible (by permission)”, so it’s the natural word for asking permission.
Могу войти? means “Am I able to come in?” (ability/capacity), and can sound less clearly like a permission request. In many contexts people still understand it as permission, but Можно войти? is the standard polite formula.

Russian often omits the subject when it’s obvious. Можно войти? literally is like “Is it allowed to enter?” The “for me” part is understood from context.

Yes. It’s an impersonal construction:

• можно = predicate meaning “allowed/possible”
• войти = infinitive “to enter”
  Together they form a full question: “Is it allowed to enter?”

Because you’re asking about a single completed action—entering once right now. That’s a typical use of the perfective infinitive: войти.
Можно входить? is possible, but it more often suggests “Is it allowed to be coming in / to enter (as a general rule)?” or can sound like you’re asking whether people may start entering (e.g., an event opening).

Literally войти is “to enter / to go in.” Russian doesn’t consistently encode “come” vs “go” the way English does; the perspective is usually inferred. In English, the natural translation in this situation is “come in.”

Common replies:

• Да, конечно. = “Yes, of course.”
• Да, входите. = “Yes, come in.” (polite/plural imperative)
• Войдите, пожалуйста. = “Come in, please.” (a bit more formal)
• Нет, нельзя. = “No, you can’t / it’s not allowed.”
• Подождите, пожалуйста. = “Please wait.”

Yes, that’s natural. Пожалуйста can go at the end or after можно:

• Можно войти, пожалуйста?
• Можно, пожалуйста, войти? (slightly more “careful” sounding)
  All are understandable; end position is very common.

It’s standard punctuation because Извините is a separate introductory word/phrase (like “Excuse me,”). In informal texts people may omit it, but in correct writing it’s usually there: Извините, можно войти?

Yes. Typically:

• ИзвинИте, with a slight pause (polite preface)
• then rising intonation on можно войтИ? to mark a yes/no question
  A flat or overly sharp intonation can sound impatient.

Yes, depending on formality:

• Можно? (at a door, with a gesture) = “May I?”
• Можно войти? = standard
• Разрешите войти? = more formal/official (“Permit me to enter?”)
• Я могу войти? = understandable but focuses more on “Can I (am I able to)…”