I agree with everything mentioned above. It's also possible to say "Хорош дрыхнуть!" "хорОш" in this instance means "enough", therefore "хватит дрыхнуть!" is another option. Дрыхнуть is very informal though, but neither offensive nor rude at all.

First, push one and then say "Не спи, замёрзнешь!" :)

Пора вставать! Вставай!

I don't think we have a formal word for this:/ Do you have separate formal/informal words in English? Разбуди меня - "Wake me up" Вставай - 'get up'. Commonly used when you are waking someone up. But is a bit different form 'wake up'. Просыпайся - wake up. Also commonly used. Possibly the least insisting option. It is imperfective, just like 'вставай'. There is a certain difference in the way perfective and imperfective are used in imperative. Imperfective is more like an _invitation_. Perfective is direct. It can be a request... an order... a practical instruction or advice etc. When you are preparing to your trip to Russia and I recommend you to take your guitar with you, I use perfective. Because it is advice or a request. When we are travelling together I say "take the guitar and let's go", i use imperfective (unless I'm _asking_ you to carry it, or instructing you or...). So it is not that imperfective is more 'polite'. It is less direct. Проснись - wake up. If 'просыпайся' invites to start the process, to _do_ something, then 'проснись' means the result: get awake. This is eactly how it is different - you think of the result, about change in state. Not about what the person should be doing.:) So it is more insisting may be. Not necessary in a bad way. What if it is said with a playful tone/in a playful context after all? Or what if waking up is in person's interests? Also it may imply urgency as it means the immediate result.

Разбуди is a request to someone. Разбуди его! Wake him up! Wake up - проснись! Get up - вставай!