После разговора с врачом мне было не до шуток.

Because после always takes the genitive.

• после разговора = after the conversation
• Base form: разговор
• Genitive singular: разговора

This is a very common pattern:

• после урока = after the lesson
• после работы = after work
• после встречи = after the meeting

So in this sentence, после разговора is simply the normal case form required by после.

It is с врачом because с meaning with takes the instrumental case.

• Base form: врач
• Instrumental singular: врачом

So:

• разговор с врачом = a conversation with the doctor

Be careful: с can mean different things, and the case depends on the meaning.

• с врачом = with the doctor → instrumental
• с работы = from work → genitive

Here it clearly means with, so instrumental is used.

Russian often uses an impersonal construction for states and feelings, where the person experiencing the state is put in the dative case.

So:

• мне = to me / for me
• literally, the structure is something like: To me, it was not joke-time

This is different from English, where we usually use a personal subject:

• English: I wasn’t in the mood for jokes
• Russian: Мне было не до шуток

This pattern is very common in Russian:

• мне холодно = I am cold
• ему скучно = he is bored
• нам было весело = we were having fun

Было is the past tense of быть, but here it appears in the neuter singular past form because the sentence is impersonal.

In impersonal sentences, Russian often uses:

• было in the past
• будет in the future
• no explicit verb in the present

Compare:

• Мне не до шуток. = I’m not in the mood for jokes.
• Мне было не до шуток. = I wasn’t in the mood for jokes.
• Мне будет не до шуток. = I won’t be in the mood for jokes.

So было does not agree with a visible subject, because there is no normal subject here.

Не до + genitive is a set expression meaning roughly:

• not in the mood for
• not up for
• not the time for
• one has more serious things to think about

It is not just the ordinary preposition до meaning until or up to. In this expression, it creates a special meaning.

Examples:

• Мне не до сна. = I’m not in the mood for sleep / I have no time for sleep.
• Ему сейчас не до разговоров. = He’s not up for talking right now.
• Нам было не до смеха. = We were in no mood for laughter.

So in your sentence, не до шуток means much more than a literal not until jokes. It is an idiomatic expression.

Because не до is followed by the genitive case, and here the natural noun form is genitive plural.

• Base form: шутка
• Genitive plural: шуток

So:

• не до шуток = not in the mood for jokes / no laughing matter

This plural is very natural in Russian because it refers to joking in general, not to one specific joke.

Usually, the idiomatic phrase is не до шуток.

Why plural?

• It refers to jokes/joking as a general activity
• It sounds like this is not a joking matter

Не до шутки is not the standard expression here. A native speaker would strongly prefer не до шуток.

Russian often uses plural nouns in idiomatic expressions where English might use a singular or an abstract phrase.

Because this is an impersonal sentence. Russian does not always need a subject like я or это.

The focus is not on who was, but on the state someone was in.

Structure:

• После разговора с врачом = after the conversation with the doctor
• мне = to me
• было не до шуток = it was not the time/mood for jokes

This kind of sentence is extremely common in Russian, especially for:

• physical states
• emotions
• necessity
• possibility
• general circumstances

Yes, the word order is natural. The sentence starts with the time/context phrase:

• После разговора с врачом = setting the scene first

Then it gives the experiencer:

• мне

Then the main predicate:

• было не до шуток

This order sounds very normal and smooth.

You could change the word order for emphasis, for example:

• Мне после разговора с врачом было не до шуток.
• Не до шуток мне было после разговора с врачом.

But the original version is probably the most neutral.

Russian has no articles, so nouns do not show a/an/the directly.

• с врачом can mean with a doctor or with the doctor

You understand which one is meant from context.

In this sentence, English might naturally say either:

• after talking to the doctor
• after talking to a doctor

Russian leaves that unspecified unless the speaker adds extra words.

Yes, but the nuance changes slightly.

• после разговора с врачом = after a conversation with the doctor
• после беседы с врачом = after a talk/discussion with the doctor; slightly more formal or reflective
• после разговора у врача = after a conversation at the doctor’s office / during the visit

So the original sentence is very natural and direct. The alternatives are possible, but they are not exact copies in tone or emphasis.