Wir kaufen das T-Shirt am Merchandise-Stand.

Because wir means we, and the verb has to match the subject.

The verb kaufen is conjugated like this:

• ich kaufe
• du kaufst
• er/sie/es kauft
• wir kaufen
• ihr kauft
• sie/Sie kaufen

So with wir, you use kaufen.

Because T-Shirt is a neuter noun in German, so its article is das.

German nouns have grammatical gender:

• der = masculine
• die = feminine
• das = neuter

So the noun is learned as das T-Shirt.

This does not mean the shirt is somehow “neutral” in real life—it is just the grammatical gender of the word.

Because das T-Shirt is the direct object of kaufen, and direct objects usually take the accusative case.

In this sentence:

• Wir = subject
• kaufen = verb
• das T-Shirt = thing being bought, so it is the direct object

For a neuter noun like das T-Shirt, the article is:

• nominative: das
• accusative: das

So it stays das T-Shirt.

am is a contraction of an dem.

• an dem → am

So:

• am Merchandise-Stand = an dem Merchandise-Stand

In this sentence it means something like at the merchandise stand.

This is very common in German. Other examples:

• am Bahnhof = at the train station
• am Fenster = at the window

Because this sentence describes a location, not movement toward a destination.

German prepositions like an can take:

• dative for location: where?
• accusative for direction/movement: where to?

Here, the idea is buying something at the stand, so it is a location:

• am Merchandise-Stand = at the merchandise stand
  (an dem, dative)

If you were talking about movement toward it, you might use accusative:

• Wir gehen an den Merchandise-Stand. = We go to the merchandise stand.

Yes. This is a very normal German main-clause word order:

• Wir = subject
• kaufen = verb
• das T-Shirt = object
• am Merchandise-Stand = place expression

A basic pattern is:

Subject + verb + other information

The most important rule is that in a normal main clause, the conjugated verb is in position 2.
That is true here:

• Wir | kaufen | das T-Shirt am Merchandise-Stand

Yes, German word order is flexible, as long as the conjugated verb stays in second position in a main clause.

For example:

• Am Merchandise-Stand kaufen wir das T-Shirt.

This puts more emphasis on the location.

But you cannot usually say:

• Wir das T-Shirt kaufen am Merchandise-Stand.

That sounds wrong in a normal main clause because kaufen must stay in second position.

Because all nouns are capitalized in German.

So in this sentence:

• T-Shirt = noun
• Merchandise-Stand = noun

Both must begin with capital letters.

This is one of the most noticeable spelling differences between English and German.

German often uses hyphens in compound nouns, especially when:

• one part is a foreign word
• the compound would be hard to read without one
• the writer wants to make the structure clearer

So Merchandise-Stand is a natural written form.

You may also see similar forms like:

• Fanshop
• Merch-Stand
• Verkaufsstand

All nouns in the compound are treated as one noun overall.

In German, the simple present often covers what English expresses with both:

• buy
• are buying

So Wir kaufen das T-Shirt can mean:

• We buy the T-shirt
• We are buying the T-shirt

depending on context.

German usually does not need a separate progressive form like English are buying.

Because German often combines the preposition and article into one word.

Here:

• an
  • dem = am

So the article the is still there—it is just built into am.

This is similar to other very common contractions:

• im = in dem
• zum = zu dem
• zur = zu der
• vom = von dem

So am Merchandise-Stand already includes the idea of at the merchandise stand.