Wir trainieren zusammen im Garten.

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Questions & Answers about Wir trainieren zusammen im Garten.

What tense and person is the verb trainieren in, and how is it conjugated for wir?
trainieren here is in the present tense (Präsens), indicative mood, first‑person plural. The infinitive is trainieren, and for wir, German verbs end in ‑en, so you get wir trainieren (we train / we are training).
What part of speech is zusammen, and can it be replaced by another word such as miteinander? Where can zusammen appear in the sentence?

zusammen is an adverbial meaning together. You can replace it with miteinander (also “together”), e.g.
  Wir trainieren miteinander im Garten.
zusammen normally follows the verb (wir trainieren zusammen), but you can also move it to the beginning or end for emphasis:
  Zusammen trainieren wir im Garten.

Why is it im Garten instead of in dem Garten, and what case is Garten in?

im is a contraction of in dem. When in indicates a location (answering “where?”), it takes the dative case. Garten is masculine, so its dative singular article is dem:
  in dem Garten → im Garten

Why is Garten capitalized?
In German, all nouns are capitalized. Garten is a noun, so it gets a capital G. Other parts of speech (verbs, adverbs, prepositions) remain lowercase.
Why isn’t there a reflexive pronoun like uns after trainieren (as in English “we train ourselves”)?
Unlike some German verbs, trainieren is not reflexive for “working out.” You simply say wir trainieren to mean “we are exercising.” Adding uns (wir trainieren uns) would sound like you’re training other people (or each other), not exercising yourselves. For a reflexive idea you’d more commonly say wir halten uns fit (we keep ourselves fit).
Could we use üben instead of trainieren here? What is the difference?

üben means to practice or rehearse, often a skill, music piece, language, etc. trainieren usually implies physical exercise or sports training. So
  Wir trainieren zusammen im Garten
suggests a workout, whereas
  Wir üben zusammen im Garten
suggests practicing something (e.g., yoga poses, sport drills).

Why is trainieren the second element in the sentence, and can we change the order of the sentence parts?

German main clauses follow the verb‑second (V2) rule: the finite verb must be the second element. Here wir (subject) is first, so trainieren is second. You can put other elements (adverbials, objects) first for emphasis, but the verb still stays in second position. For example:
  Im Garten trainieren wir zusammen.
  Zusammen trainieren wir im Garten.