Bevor wir anfangen, nimmt jede Person ihr Namensschild und setzt sich an den richtigen Platz.

Because bevor introduces a subordinate clause. In German, the conjugated verb usually goes to the end of a subordinate clause.

So:

• wir fangen an = main clause word order
• bevor wir anfangen = subordinate clause word order

Notice that with anfangen, the separable prefix an- rejoins the verb in subordinate clauses:

• Main clause: Wir fangen an.
• Subordinate clause: ..., bevor wir anfangen.

That is very common with separable verbs in German.

Because the sentence begins with a subordinate clause: Bevor wir anfangen.

When a subordinate clause comes first, the main clause follows, and German still keeps the finite verb in the second position overall. Since the first position is already occupied by the whole clause Bevor wir anfangen, the verb comes next:

• Bevor wir anfangen, nimmt jede Person ...

This is the same pattern you see in sentences like:

• Heute geht er nach Hause.
• Wenn ich Zeit habe, gehe ich nach Hause.

In both cases, something else takes the first position, so the verb comes before the subject.

Because the subject is jede Person, which is grammatically singular.

Even though jede Person refers to all people one by one, the head noun Person is singular, so the verb must also be singular:

• jede Person nimmt
• not jede Person nehmen

This is similar to English each person takes, not each person take.

ihr Namensschild is in the accusative case, because it is the direct object of nimmt.

But Namensschild is a neuter noun: das Namensschild. In the accusative, neuter articles and possessives look the same as in the nominative:

• nominative: ihr Namensschild
• accusative: ihr Namensschild

So it is not ihren, because ihren would be used with a masculine plural or certain other forms, not with a neuter singular noun like Namensschild.

Compare:

• Sie nimmt ihr Namensschild.
• Sie nimmt ihren Stift.
  because der Stift is masculine

Not necessarily. Here ihr means his/her/their own, depending on the person being referred to.

Since the subject is jede Person, German uses ihr Namensschild to mean that each person takes their own name tag.

This is one place where German and English do not match perfectly word for word. In English, we often say their name tag for gender-neutral singular reference. German commonly uses the possessive that agrees with the noun and the intended possessor in context.

The important thing here is that ihr matches Namensschild in form, and the sentence means each person takes the name tag belonging to that person.

Sich setzen is a reflexive verb meaning to sit down or to seat oneself.

So:

• setzen = to set, place
• sich setzen = to sit down

In this sentence:

• setzt sich an den richtigen Platz

means the person moves into a seat or takes their place.

The reflexive pronoun sich is required here because this is the standard verb form. You cannot normally just say setzt an den richtigen Platz with this meaning.

Because this sentence describes movement toward a place, not being already located there.

German two-way prepositions like an use:

• accusative for direction/movement
• dative for location

Here, the person is sitting down into/to the correct place, so German uses the accusative:

• an den richtigen Platz

If the meaning were static location, it would be dative:

• Die Person sitzt an dem richtigen Platz.
  = The person is sitting in the correct place.

So:

• sich setzen an + accusative = movement
• sitzen an + dative = location

Because Platz is masculine: der Platz.

After the preposition an with movement, we need the accusative case:

• masculine accusative article: den
• adjective after den takes -en

So:

• an den richtigen Platz

Breakdown:

• an = preposition
• den = masculine accusative article
• richtigen = adjective with weak ending -en
• Platz = noun

This is a very standard pattern in German:

• in den großen Raum
• auf den alten Stuhl
• an den richtigen Platz

Because the same subject, jede Person, applies to both verbs:

• nimmt
• setzt sich

German, like English, does not need to repeat the subject when two verbs are connected by und and have the same subject.

So this is understood as:

• jede Person nimmt ihr Namensschild und setzt sich an den richtigen Platz

You could repeat it, but that would usually sound unnecessary:

• ..., nimmt jede Person ihr Namensschild und jede Person setzt sich ...

That is grammatical, but much less natural.

Because German uses a comma to separate a subordinate clause from the main clause.

Here:

• Bevor wir anfangen = subordinate clause
• nimmt jede Person ihr Namensschild ... = main clause

So the comma is required:

• Bevor wir anfangen, nimmt jede Person ...

This is a very important punctuation rule in German. Subordinate clauses are normally separated by commas.

Both can mean to begin or to start.

So you could also say:

• Bevor wir beginnen, ...

The difference is mostly style and usage:

• anfangen is very common and conversational
• beginnen is a bit more formal or neutral in tone

In this sentence, anfangen sounds natural and everyday.

Jede Person emphasizes the action individually: each person does it.

• jede Person = each person
• alle Personen = all people

Both can be possible in some contexts, but the focus is slightly different:

• Jede Person nimmt ihr Namensschild ...
  = one by one, every individual does this
• Alle Personen nehmen ihre Namensschilder ...
  = all of them do this

The version with jede Person is very natural for instructions, especially when you want to make clear that this applies to everyone individually.

No, that would not be correct here.

With nehmen, you normally do not use a reflexive pronoun for this meaning. The correct form is:

• jede Person nimmt ihr Namensschild

The reflexive belongs with sich setzen, not with nehmen.

So the structure is:

• nimmt
  • direct object
• setzt sich
  • place expression

Only the second verb is reflexive.