Learn Hardcore Russian: Мой друг часто приезжает в наш город.

In Russian, possessive adjectives agree in gender with the noun they describe.
Друг is a masculine noun, so you must use the masculine form мой.

masculine: мой друг – my friend (male)
feminine: моя подруга – my (female) friend
neuter: моё письмо – my letter

So мой друг is grammatically correct because друг is masculine.

Why is друг in the form друг and not друга (e.g. моего друга)?

Друг is the subject of the sentence, so it stands in the nominative case.
Nominative answers “who?/what?”: Кто часто приезжает? – Мой друг.

Друга / моего друга would be a different case (genitive/accusative), used for objects or after some prepositions, e.g.:

Я жду друга. – I’m waiting for (my) friend.
Here, your friend is the object, not the subject, so a different case is used.

What is the difference between приезжает and приходит here?

Both mean “comes/arrives,” but there is a nuance:

приезжать / приехать – to arrive by some means of transport (car, train, bus, etc.)
приходить / прийти – to arrive on foot, or more generally “to come (walking)”

So Мой друг часто приезжает в наш город suggests your friend usually comes to your city by transport.
If you said Мой друг часто приходит ко мне, that would more naturally describe someone coming to your house on foot (or the manner of coming is not focused on transport).

Why is it приезжает (imperfective) and not приедет or приехал (perfective)?

Russian uses imperfective verbs for repeated, habitual actions.
Приезжает (from приезжать) shows that this is something your friend does regularly or often.

Мой друг часто приезжает в наш город. – He often comes (habitually).
Мой друг приедет в наш город. – He will come (one future occasion).
Мой друг приехал в наш город. – He came (one finished event in the past).

So приезжает is chosen because the sentence talks about a repeated action, not a single visit.

Why not use ездит instead of приезжает?

Ездить means “to go (by transport), to travel (there and back, in general)”, while приезжать focuses on the arrival.

Compare:

Мой друг часто ездит в наш город. – He often travels to our city (in general; the whole trips).
Мой друг часто приезжает в наш город. – He often comes to / arrives in our city (emphasis on the fact he arrives here).

Both are possible, but приезжает highlights the arrival into your city more strongly.

Why is it в наш город and not в нашем городе?

With motion into a place, Russian uses в + accusative.
So you say: приезжать в город – to come/arrive to the city.

в наш город – to our city (motion into it, accusative)
в нашем городе – in our city (location inside it, prepositional)

Compare:

Мой друг живёт в нашем городе. – My friend lives in our city.
Мой друг часто приезжает в наш город. – My friend often comes to our city.

What exactly does в наш город mean compared to к нам?

Both can be translated as “to us / to our place,” but they focus on different things:

в наш город – literally “into our city”; emphasizes the city as a location.
к нам – “to us”; emphasizes the people (us), not the city.

So:

Мой друг часто приезжает в наш город. – He often comes to our city.
Мой друг часто приезжает к нам. – He often comes to us (to where we are).

You can even combine them: приезжает к нам в наш город, but that’s usually more than you need in everyday speech.

Why is город not changed in form after в? It’s still город, not города or городе.

Here, город is in the accusative case, masculine inanimate.
For masculine inanimate nouns, the accusative form is the same as the nominative.

So:

nominative: город – the city
accusative: в город – into the city

By contrast, with feminine nouns or some other genders, the form would change, e.g.:

в деревню (from деревня – village)

Why is the adverb часто placed before the verb? Can I move it?

The most neutral position for часто is before the verb:
Мой друг часто приезжает в наш город.

You can move it, but word order affects emphasis:

Мой друг приезжает в наш город часто. – more emphasis on how often he comes; sounds a bit more marked or contrastive.
Часто мой друг приезжает в наш город. – strong emphasis on the frequency “often” at the start of the sentence.

Grammatically, all are possible, but the original order is the most natural and neutral.

Why is the verb приезжает singular and not plural like приезжают?

The verb must agree in number with the subject.
The subject мой друг is singular, so the verb must be 3rd person singular: он приезжает.

If the subject were plural, the verb would change:

Мои друзья часто приезжают в наш город. – My friends often come to our city.

Could I say Друг мой часто приезжает в наш город instead of Мой друг…?

Yes, Друг мой… is grammatically correct, but it sounds more poetic, emotional, or old-fashioned in modern Russian.
In normal neutral speech, people almost always say Мой друг….

So:

Мой друг часто приезжает… – neutral, standard.
Друг мой, часто приезжаешь ты… – poetic style, special emphasis on “friend”.

How do you pronounce приезжает, and why is it written with е and not ё?

Приезжает is pronounced approximately as [pr-ee-iz-ZHA-yet], with the main stress on -жа́-: приезжа́ет.
The жж sounds like a long “zh”: [zh] as in “measure,” doubled.

Russian often writes ё as е in normal orthography, especially in unstressed or predictable positions.
Here it’s written приезжает, but the stressed syllable sounds like -жа́-, not -же-.
In dictionaries you might see приезжа́ет with stress marked, but in running text, you just have to know the correct stress and pronunciation.