Learn Hardcore German: Der Nachbar gratuliert mir zum neuen Zaun und schenkt mir mehrere Pinsel. - The neighbor congratulates me on the new fence and gives me several brushes.

In German, gratulieren (to congratulate) takes zu + Dativ to introduce the occasion or reason: you congratulate someone on something.
zum is simply the contraction of zu
- dem (dative masculine definite article).
Since Zaun is masculine (der Zaun), dative singular is dem Zaun, so zu + dem Zaun = zum Zaun.

How do you decline the adjective neu after zum in the dative?

Here dem is a weak (definite) article carrying the grammatical information, so the adjective uses the weak ending -en.
Paradigm for der Zaun:
• Nominative: der neue Zaun
• Dative: dem neuen Zaun → zum neuen Zaun

Why does gratulieren take mir, and what case is mir?

gratulieren is one of the German verbs that assign the person being congratulated to the dative case.
mir is the dative form of ich. You cannot use the accusative mich here.

Why does schenken use both mir and mehrere Pinsel? What cases are these?

schenken is ditransitive: it takes an indirect object (the recipient) in the dative and a direct object (the gift) in the accusative.
In our sentence:
• mir = dative (recipient)
• mehrere Pinsel = accusative (what is given)

Why is it mehrere Pinsel and not mehr Pinsel or viele Pinsel?

mehrere means “several” and is used to say “a number of” items. It always requires a plural noun.
mehr means “more” (comparative: “more brushes than before”) and is not the same as “several.”
viele means “many” and is also grammatical (“viele Pinsel”) but carries a slightly different nuance (“a lot of brushes” vs. “several brushes”).

Why doesn’t Pinsel change its ending in the plural?

Some German nouns form the plural without adding an ending or umlaut.
der Pinsel becomes die Pinsel in the plural with no change to the stem.
You recognize the plural by the article die and context (e.g., mehrere).

Why is the second verb schenkt placed immediately after und instead of at the end of the sentence?

The sentence has two main clauses joined by the coordinating conjunction und.
In each clause, German follows the Verb-Second (V2) rule: the finite verb occupies the second position.
Clause 1: Der Nachbar (1) gratuliert (2) mir zum neuen Zaun.
Clause 2: und (conj.) schenkt (2) mir mehrere Pinsel.

Can I swap the two clauses, saying “Der Nachbar schenkt mir mehrere Pinsel und gratuliert mir zum neuen Zaun”?

Yes. When you swap the clauses, both still follow V2 word order:

Der Nachbar schenkt mir mehrere Pinsel (Clause 1).
und gratuliert mir zum neuen Zaun (Clause 2).
The nuance doesn’t change much; it simply shifts the emphasis to the gift before the congratulations.

Is there an alternative to gratulieren, like beglückwünschen?

Yes, jemandem zu etwas beglückwünschen is a synonym and slightly more formal.
It uses the same pattern: dative for the person and zu + Dativ for the occasion (e.g., Er beglückwünscht mich zum neuen Zaun).