Am Dienstag kaufe ich frisches Gemüse im Supermarkt.

In German, to express “on Tuesday,” you normally combine the preposition an with the definite article dem, giving an dem. This contracts to am. So:

• am Dienstag = “on Tuesday.”
  You wouldn’t say just Dienstag for a specific day unless it’s part of a larger phrase (e.g. “nächsten Dienstag”).

German is a V2 (verb-second) language: the conjugated verb must occupy the second “slot” in a main clause. If you start with a time expression like am Dienstag, that counts as the first slot. The verb then comes immediately after, causing a subject–verb inversion:

1. Slot 1: Am Dienstag
2. Slot 2: kaufe
3. Slot 3: ich
   Rest of the sentence follows.

Yes. If you begin with the subject ich, the verb still stays in second place:

1. Slot 1: Ich
2. Slot 2: kaufe
3. Slot 3: am Dienstag
   …so both word orders are correct—the difference is only emphasis (time first vs. subject first).

This is a strong adjective ending. Rules at work:

• Gemüse is neuter (das Gemüse).
• In our sentence, Gemüse is the direct object, so it’s accusative.
• There is no article before Gemüse, so the adjective must carry the case and gender information itself.
  For neuter accusative, strong declension uses -es, hence frisches Gemüse.

im is a contraction of in dem. It’s the combination of the preposition in (meaning “in” or “at”) plus the dative article dem (because der Supermarkt is masculine). So:

• in dem Supermarkt → im Supermarkt = “at/in the supermarket.”