Learn Hardcore German: Langfristig sparen wir Geld, wenn wir monatlich einkaufen. - In the long term we save money if we shop monthly.

German main clauses have the verb in second position (the V2 rule). If you put something other than the subject in the first position—here, the adverb Langfristig—the subject and verb invert:

Wir sparen langfristig Geld.
Langfristig sparen wir Geld. Both are correct; the finite verb (sparen) must be the second element.

Why is there a comma before wenn, and what does it do?

A comma is mandatory before a subordinate clause in German. Wenn introduces a subordinate (conditional/temporal) clause and forces verb-final word order in that clause:

Langfristig sparen wir Geld, wenn wir monatlich einkaufen. If the wenn-clause comes first, you still need a comma:
Wenn wir monatlich einkaufen, sparen wir langfristig Geld.

Does wenn mean “if” or “when” here? How is it different from falls and wann?

wenn = “if” (conditional) or “when/whenever” (repeated/general time). In this sentence it’s conditional/habitual.
falls = “if” only (purely conditional; often more hypothetical/formal).
wann is used for direct or indirect questions about time, not for conditions. Examples:
Wenn wir monatlich einkaufen, sparen wir Geld. (if/whenever)
Falls wir monatlich einkaufen, sparen wir Geld. (if—possibly more tentative)
Wann kaufen wir ein? (When do we shop?)

Why is there no article before Geld?

Geld is an uncountable (mass) noun, and German normally omits an article in general statements:

Wir sparen Geld. Use an article only when referring to specific, known money:
Wir sparen das Geld für die Reise. You can also say:
Wir sparen etwas Geld.
Wir sparen kein Geld. (negative with kein)

Why is einkaufen at the very end of the clause? Is that an infinitive?

In subordinate clauses, the finite verb goes to the end. With separable verbs like einkaufen, the prefix (ein) stays attached at the end: … wenn wir monatlich einkaufen. It looks like an infinitive, but for wir the present-tense ending is also -en, so it happens to match the infinitive form. You see the difference with other persons:

… wenn ich monatlich einkaufe.
… wenn er monatlich einkauft.

What’s the difference between einkaufen and kaufen?

einkaufen = to go shopping (for groceries/everyday goods), often without naming a specific item.
- Wir kaufen samstags ein.
kaufen = to buy (a specific thing).
- Wir kaufen ein Auto. You can combine einkaufen with a place:
Ich kaufe im Supermarkt ein.

Is monatlich the most natural choice? What are good alternatives?

Monatlich is correct and concise, slightly formal/neutral. Common alternatives:

jeden Monat (every month)
einmal im Monat (once a month; emphasizes the single monthly trip)
pro Monat (per month; a bit formal/technical) More idiomatic variants:
Langfristig sparen wir Geld, wenn wir jeden Monat einkaufen.
Langfristig sparen wir Geld, wenn wir nur einmal im Monat einkaufen (gehen).
Langfristig sparen wir Geld, wenn wir monatlich Großeinkauf machen.

Where should monatlich go in the sentence?

In the subordinate clause, placing it before the verb is natural:

… wenn wir monatlich einkaufen. In a main clause with einkaufen, a common placement is before the verb bracket:
Wir kaufen monatlich ein. With other adverbials, time tends to come early:
Wir kaufen einmal im Monat im Supermarkt ein. (time before place)

Can the wenn-clause come first?

Yes:

Wenn wir monatlich einkaufen, sparen wir langfristig Geld. Remember, after a fronted subordinate clause, the main clause still follows V2 order, so sparen comes before wir.

Why present tense instead of future or conditional? Could we use würden?

German present tense often expresses general truths and habitual results, which fits here. Use the conditional for a hypothetical scenario:

Real/general: Langfristig sparen wir Geld, wenn wir monatlich einkaufen.
Hypothetical: Langfristig würden wir Geld sparen, wenn wir monatlich einkaufen würden. Using würden in both clauses is common in hypothetical statements; you can also keep the wenn-clause in the present in many contexts.

Is langfristig an adverb here? Any synonyms?

Yes, it’s an adverb (normally lowercase; capitalized only because it starts the sentence). As an adjective: langfristige Planung. Natural paraphrases:

auf lange Sicht
auf Dauer
Contrast: kurzfristig, mittelfristig

Can I say einsparen or ersparen instead of sparen?

Different nuances:

sparen = to save (money/time) in general. Best here: Wir sparen Geld.
einsparen = to cut/reduce expenditures or consumption (more formal/technical): Wir sparen Kosten ein.
ersparen = to spare someone something (Dat + Akk): Das erspart uns Wege/Zeit. For this sentence, stick with sparen.

Can I drop the second wir in the wenn-clause?

No. German requires an explicit subject in finite clauses. You need wenn wir …. You could use impersonal man if you want a general statement:

Langfristig spart man Geld, wenn man monatlich einkauft.

Can I say einkaufen gehen? Is there a difference?

Yes:

… wenn wir monatlich einkaufen gehen. This emphasizes the act of going out to do the shopping; it’s a bit more colloquial. In that subordinate clause, the finite verb gehen still goes to the end. Both einkaufen and einkaufen gehen are fine; the meaning difference is minimal here.