Он член нашей команды.

In Russian, the verb to be is usually omitted in the present tense.

So:

• Он член нашей команды. = He is a member of our team.

There is no present-tense есть here in normal usage.

Compare:

• Он студент. = He is a student.
• Она врач. = She is a doctor.

Russian does use forms of быть in the past and future:

• Он был членом нашей команды. = He was a member of our team.
• Он будет членом нашей команды. = He will be a member of our team.

So the missing is is completely normal.

Член is in the nominative singular form.

Here it works as a predicate noun: it tells us what he is.

• Он = he
• член = member

In present-tense sentences without быть, Russian often uses the nominative for this kind of predicate:

• Он студент.
• Она учитель.
• Он член нашей команды.

So член is just the basic dictionary form here.

Because член usually takes the genitive case for the group or organization someone belongs to.

So Russian says literally:

• member of our team

That gives:

• член команды = member of a/the team
• член нашей команды = member of our team

Here:

• команда → команды because it is in the genitive singular
• наша → нашей because the adjective must agree with команды

So the pattern is:

• член + genitive

Examples:

• член семьи = member of the family
• член клуба = member of the club
• член группы = member of the group

Because it agrees with команды, which is:

• feminine
• singular
• genitive

The noun is:

• команда = team

In the genitive singular:

• команда → команды

The possessive adjective наша must match that noun, so:

• наша команда = our team
• нашей команды = of our team

This is standard adjective agreement in Russian.

Yes, and that is often very natural.

The difference is:

• Он член нашей команды. = He is a member of our team.
  This stresses membership/status a bit more.
• Он в нашей команде. = He is on our team / in our team.
  This is often more conversational and can sound less formal.

So both are correct, but they are not exactly identical in tone.

The given order is the most neutral:

• Он член нашей команды.

Russian word order is flexible, but changing it changes the emphasis.

For example:

• Он член нашей команды.
  Neutral statement.
• Член нашей команды он.
  Stronger emphasis on member of our team; less neutral.
• Он — член нашей команды.
  Same basic meaning, but the dash can add emphasis in writing.

So the original word order is a good default choice.

Russian has no articles.

So член can mean:

• a member
• the member

The exact meaning depends on context.

In this sentence, English naturally uses:

• He is a member of our team.

But Russian does not need any separate word for a.

A helpful approximation is:

• Он — on
• член — roughly chlyen
• нашей — roughly NA-shey
• команды — roughly ka-MAN-dy

Stress:

• он
• член
• на́шей
• кома́нды

A smoother whole-sentence approximation:

• On chlyen NA-shey ka-MAN-dy

The hardest word for many English speakers is член, because of the consonant cluster at the beginning.

Usually yes, but with one important warning.

In normal contexts, член means:

• member of a team
• member of a club
• member of a group
• member of parliament, etc.

However, in some contexts, член can also mean penis, especially in biology, medicine, or crude/joking usage.

That does not make this sentence wrong or funny in normal use:

• Он член нашей команды. is completely standard.

Still, learners sometimes notice the other meaning, so it is useful to be aware of it.

Normally, no.

• Он есть член нашей команды is not standard everyday Russian for He is a member of our team.

Modern Russian usually leaves out is in present-tense identity/classification sentences.

The word есть does exist, but in modern usage it usually has other functions, such as meaning there is/are or giving strong emphasis in special contexts.

So for this sentence, stick with:

• Он член нашей команды.

Он is in the nominative case, because it is the subject of the sentence.

Basic breakdown:

• Он — nominative, subject
• член — nominative, predicate noun
• нашей команды — genitive phrase after член

So even though the sentence is short, it shows two important Russian patterns at once:

1. no present-tense to be
2. член + genitive for member of ...