Learn Hardcore Russian: Хороший собеседник внимательно слушает и честно отвечает. - A good interlocutor listens attentively and answers honestly.

Whether you translate Хороший собеседник as a good conversationalist or the good conversationalist depends entirely on context, not on any special Russian word. Here it means something general, so a good conversationalist is the natural English translation, but the Russian phrase itself is neutral with respect to definiteness.

Why is it хороший and not хорошо?

Хороший is an adjective; хорошо is an adverb (and also the short-form neuter adjective in some contexts).

Хороший собеседник = a good conversationalist. Хороший describes the noun собеседник, so you must use the adjective form.
Хорошо слушает = listens well. Here хорошо would describe the verb слушает, so the adverb form is used.

In this sentence, хороший agrees with собеседник in:

gender: masculine
number: singular
case: nominative

So хороший is the correct form.

What case is собеседник in, and why?

Собеседник here is in the nominative singular.

Reasons:

It is the subject of the sentence: Хороший собеседник (кто?) слушает и отвечает.
The base dictionary form of a noun is also nominative singular, and собеседник appears in exactly that form.

So хороший собеседник is a simple nominative subject phrase: a good conversationalist.

Why is there no он or она? Who is doing the action?

The subject is хороший собеседник itself, so a pronoun is not needed.

The sentence structure is:

Хороший собеседник – subject
внимательно слушает и честно отвечает – predicate (what the subject does)

In English we might expect something like:
A good conversationalist listens carefully and answers honestly.
Russian does not need an extra он/она because собеседник already gives the subject explicitly.

For general statements about people, Russian very often uses a singular noun as the subject like this:

Хороший учитель понимает учеников. – A good teacher understands students.
Настоящий друг всегда помогает. – A true friend always helps.

Are внимательно and честно adjectives or adverbs? How are they formed?

Внимательно and честно are adverbs.

They are formed from adjectives:

внимательный (attentive) → внимательно (attentively, carefully)
честный (honest) → честно (honestly)

This -о ending is a very common way to form adverbs from adjectives in Russian, similar to English -ly:

быстрый → быстро (fast → quickly)
тихий → тихо (quiet → quietly)

In the sentence:

внимательно modifies слушает
честно modifies отвечает

Why do the adverbs come after the verbs: слушает внимательно vs внимательно слушает?

In the given sentence, the adverbs actually come before the verbs:

внимательно слушает
честно отвечает

This is the most neutral, common position for such adverbs in Russian: adverb + verb.

Other word orders are sometimes possible, but they change the rhythm or add emphasis. For example:

Слушает внимательно и отвечает честно. – slightly more emphasis on the actions.
Он внимательно слушает. – also neutral.

So внимательно слушает and честно отвечает are the standard, natural orders here.

Why is it слушает, not слушают?

The verb must agree with the subject in number and person.

Subject: хороший собеседник – masculine, singular
So the verb is 3rd person singular: он слушает

If the subject were plural, the verb would change:

Хорошие собеседники внимательно слушают и честно отвечают.
(Good conversationalists listen carefully and answer honestly.)

So слушает (singular) is correct with собеседник (singular).

What is the difference between слушать and слышать?

They are related but not the same:

слушать – to listen (an intentional action)
- слушать музыку – to listen to music
- слушать собеседника – to listen to the person you are talking with
слышать – to hear (to perceive sound, not necessarily intentionally)
- Я слышу музыку. – I hear music.
- Я тебя плохо слышу. – I cannot hear you well.

In our sentence, внимательно слушает emphasizes the active, deliberate effort to listen carefully, so слушать is the right verb.

Why is it отвечает, not something like ответит? Is this about aspect?

Yes, this is mainly an aspect choice.

отвечать – imperfective, focuses on the process / repeated action
ответить – perfective, focuses on one completed act of answering

In the present tense, Russian normally uses only imperfective to talk about general, habitual actions:

Хороший собеседник внимательно слушает и честно отвечает.
A good conversationalist (habitually) listens carefully and answers honestly.

A perfective form like ответит would be used for a specific one-time future result:

Он честно ответит на твой вопрос. – He will answer your question honestly. (one time, in the future)

Why is there no comma before и in слушает и честно отвечает?

Here и connects two verbs with the same subject – a compound predicate:

Хороший собеседник (subject)
слушает и (слушает?) отвечает (two actions of that subject)

In Russian, when two simple predicates share the same subject and are joined by и, a comma is not used:

Он читает и пишет.
Она поёт и танцует.

A comma before и would usually appear when two independent clauses are joined (each with its own subject), but that is not the case here.

Can I change the word order, for example: Собеседник внимательно слушает и честно отвечает?

Yes, you can change the word order without changing the basic meaning, though emphasis may shift slightly.

Some natural variants:

Собеседник внимательно слушает и честно отвечает.
(A bit more neutral, without highlighting that he is good.)
Хороший собеседник честно отвечает и внимательно слушает.
(Slight emphasis on честно отвечает, just by order.)
Внимательно слушает и честно отвечает хороший собеседник.
(Strong emphasis on the actions; the subject comes at the end.)

Russian word order is relatively flexible, but the original Хороший собеседник внимательно слушает и честно отвечает
sounds very natural and neutral.

How would I say this in the plural: Good conversationalists listen carefully and answer honestly?

You need to make both the adjective and the noun plural, and the verbs plural as well:

Хорошие собеседники внимательно слушают и честно отвечают.

Changes:

хороший → хорошие (masculine plural nominative)
собеседник → собеседники (plural)
слушает → слушают (3rd person plural)
отвечает → отвечают (3rd person plural)

Is собеседник always male? How do I refer to a female conversational partner?

Grammatically, собеседник is a masculine noun, but it can refer to a person of any gender, much like человек.

If you specifically want to emphasize that the person is female, you can use the feminine form:

собеседница – a female conversationalist / interlocutor

Examples:

Мой собеседник был очень вежлив. – My (male or unspecified) interlocutor was very polite.
Моя собеседница внимательно слушала. – My female interlocutor listened attentively.