Ты можешь написать мне когда угодно, даже поздно вечером.

Ты is the informal singular you. It is used with friends, family, children, romantic partners, or people you are on informal terms with.

If you wanted the polite/formal version, you would say:

Вы можете написать мне когда угодно, даже поздно вечером.

So the choice of ты tells you something about the relationship between the speakers.

Можешь написать means you can write/message in the sense of you are free to do it or it is okay to do it.

This structure is very common in Russian:

• мочь + infinitive = can / be able to + verb

So:

• можешь написать = you can write / you may write

Using пишешь would mean you write / are writing, which does not express permission or possibility.

Можешь писать is possible in some contexts, but it sounds a bit different.
Here, написать is perfective, so it focuses on a complete act: send me a message / write to me. That is why it sounds natural here.

This is an aspect question.

• писать = imperfective
• написать = perfective

In this sentence, the speaker means you can send me a message at any time or you can write to me whenever you want, referring to a whole completed action. Russian often prefers the perfective infinitive after мочь when talking about one complete action.

So:

• можешь написать = you can write/send me a message
• можешь писать = you can be writing / you can write in general, with more focus on process or repeated activity

In everyday speech, можешь написать мне is the most natural choice here.

Because мне is the dative case, and the verb писать / написать often takes the person receiving the message in the dative.

Compare:

• написать мне = write to me
• написать ему = write to him
• написать ей = write to her

So Russian expresses this as write to someone, even though English often just says write someone.

That is why мне is correct here.

Yes. Russian word order is flexible.

All of these are natural:

• Ты можешь написать мне когда угодно...
• Ты можешь мне написать когда угодно...
• Мне ты можешь написать когда угодно...
  (more emphasis on to me)

The original order is neutral and natural.
Moving мне before написать often sounds slightly more conversational.

Когда угодно means whenever you want, any time, or at any time.

Literally:

• когда = when
• угодно = something like pleases / is acceptable, but in this expression it is fixed and idiomatic

So когда угодно is a set phrase meaning:

• any time
• whenever you like
• whenever you want

You do not usually analyze угодно literally in normal conversation; it is best learned as part of the whole expression.

Because когда угодно is already a complete adverbial expression meaning at any time / whenever.

English often uses a preposition, as in at any time, but Russian does not need one here.

Other similar Russian expressions also work without extra prepositions:

• где угодно = anywhere
• кому угодно = to anyone / anyone at all
• что угодно = anything

So когда угодно functions as a self-contained phrase.

Вечером is the instrumental case of вечер.

Russian often uses the instrumental case with parts of the day to mean in the morning / in the afternoon / in the evening / at night:

• утром = in the morning
• днём = during the day / in the afternoon
• вечером = in the evening
• ночью = at night

So поздно вечером means late in the evening.

This is a very common time expression pattern, and it often appears without a preposition.

Because поздно here is an adverb meaning late, and it modifies the whole time expression:

• поздно вечером = late in the evening

This is the most common and natural way to say it.

Поздним вечером is also possible, but it is more literary or descriptive, more like on a late evening or later in the evening depending on context. In everyday speech, поздно вечером is much more common.

It can absolutely mean send a message, text, or write to someone in a modern everyday sense.

In context, Ты можешь написать мне когда угодно very often means:

• you can text me anytime
• you can message me anytime
• you can write to me anytime

Russian написать is used broadly for written communication, not just handwriting or formal letters.

The comma separates an added clarifying or emphasizing phrase.

The main idea is:

• Ты можешь написать мне когда угодно = You can write to me anytime

Then the speaker adds:

• даже поздно вечером = even late in the evening

So the comma helps mark this as an extra emphasis or afterthought: any time — even late in the evening.

In practice, punctuation around phrases like this can vary a little depending on style, but the comma here is natural and helps readability.

Yes, but the meaning and tone would shift slightly.

• Ты можешь написать мне когда угодно... = You can write to me anytime...
• Мне можно написать когда угодно... = It is okay to write to me anytime...

With можешь, the sentence is more direct and personal: the speaker is addressing you.

With можно, the sentence sounds a little more impersonal, like stating that something is allowed.

Both are natural, but ты можешь fits especially well when speaking warmly and directly to one person.

Not exactly in the strict tense sense, but it is about general permission or possibility from now on.

Russian present-tense можешь plus infinitive often covers meanings that English expresses with can:

• present ability
• permission
• general possibility

So here it means something like:

• from now on, whenever you want, it is fine to write to me

It is not limited to one exact future moment; it expresses an open ongoing permission.