Wij bewonderen regenbogen in de tuin.

In Dutch main clauses, the finite verb usually occupies the second position (V2 rule). The subject (Wij) takes first place, so bewonderen follows it as the second element. If you start with something else (e.g., a time adverb), the verb still comes second and the subject moves to third:
Vandaag bewonderen wij regenbogen in de tuin.

Yes. We is the unstressed, informal version of wij. They both mean “we,” but wij adds emphasis or formality (common in writing). So:
We bewonderen regenbogen in de tuin.

Dutch omits articles for indefinite plurals. English “we admire rainbows” doesn’t need “some,” and neither does Dutch. If you want to say “a few rainbows,” you can use een paar:
Wij bewonderen een paar regenbogen in de tuin.

All singular nouns in Dutch are either “de”-words or “het”-words. Tuin belongs to the “de” group, so its definite article is de. If you meant “a garden” (non-specific), you’d use een tuin:
Wij bewonderen regenbogen in een tuin.

Yes. Onze is the possessive adjective “our” for plural or “de”-words. So:
Wij bewonderen regenbogen in onze tuin.
This emphasizes that it’s specifically our garden.

No, Dutch is not a pro-drop language like Spanish or Italian. You must include wij or we in declarative sentences:
✔️ Wij bewonderen regenbogen in de tuin.
A sentence starting directly with the verb (Bewonderen regenbogen…) would be ungrammatical, unless you’re forming a question (Bewonderen wij regenbogen…?) or using an imperative.