Learn Hardcore Russian: Я пишу сообщение другу.

Because Russian uses cases to show grammatical roles. другу is in the dative case to mark the indirect object (“to whom” the message is written). друг (friend) is declined:

nom друг
gen друга
dat другу
acc друга
inst другом
prep друге
Use the dative for recipients, like “to someone.”

Why is сообщение in the accusative case?

Because it’s the direct object – what you are writing. сообщение is a neuter inanimate noun, so its accusative form is identical to the nominative: сообщение.

Why isn’t there a preposition “to” before другу?

In Russian, cases replace many English prepositions. The dative case alone conveys “to someone,” so no separate preposition is needed.

What is the infinitive and aspect of пишу? How is it conjugated?

The infinitive is писать (imperfective). Imperfective verbs denote ongoing or habitual actions. Conjugation in the present tense:
я пишу
ты пишешь
он/она пишет
мы пишем
вы пишете
они пишут

What is the difference between писать and написать?

писать is imperfective (focus on the process), написать is perfective (focus on completion).
Use писать to say “I am writing” or habitual “I write,” and написать to say “I will write” or “I have written.”

Can the word order change? Why is it Я пишу сообщение другу?

Russian word order is flexible due to cases. The neutral (unmarked) order is Subject – Verb – Direct Object – Indirect Object: Я пишу сообщение другу. You can rearrange for emphasis:
Я другу пишу сообщение (emphasizes “to my friend”)
Сообщение другу я пишу (emphasizes what is being written).

Where is the stress in сообщение and how is it pronounced?

сообщение is pronounced [səɐˈbɕːenʲɪjə], with the stress on the third syllable: сообще́ние.

How do I say “my friend” in the dative case?

Add the possessive мой in the appropriate form. For masculine singular dative: моему другу, so “I am writing a message to my friend” is Я пишу сообщение моему другу.