Learn Hardcore German: Seit dem neuen Wasserfilter trinke ich fast nur noch Leitungswasser und kaufe selten Flaschen. - Since the new water filter I almost only drink tap water and rarely buy bottles.

Wasserfilter is masculine.
Dative singular masculine definite article = dem.
With a definite article in the dative, the adjective ending is -en, so neuen.

So:

Nominative: der neue Wasserfilter
Accusative: den neuen Wasserfilter
Dative: dem neuen Wasserfilter ✅ (required after seit)

That’s why it must be dem neuen Wasserfilter here.

What exactly does Seit dem neuen Wasserfilter mean? It sounds like something is missing.

You’re right: it is a shortened / elliptical expression.

Literally expanded, it would be something like:

Seit ich den neuen Wasserfilter habe, …
Seit wir den neuen Wasserfilter benutzen, …

In everyday German, people often shorten time expressions like this:

Seit dem neuen Chef … = Since we have the new boss …
Seit der Renovierung … = Since the renovation …

So Seit dem neuen Wasserfilter really means Since I/we got the new water filter / started using the new water filter.

Why is the verb trinke in second position after Seit dem neuen Wasserfilter?

German main clauses follow the verb-second (V2) rule: the finite verb must be in second position, but “position” means second element, not second word.

In this sentence:

First element: Seit dem neuen Wasserfilter (a whole prepositional phrase)
Second element: trinke (the finite verb)
Then: ich fast nur noch Leitungswasser und kaufe selten Flaschen

So the structure is:

[Time phrase] – Seit dem neuen Wasserfilter
[Verb] – trinke
[Subject] – ich
[Rest of the sentence]

This is perfectly standard German word order.

Could I also say Ich trinke seit dem neuen Wasserfilter fast nur noch Leitungswasser …? Is that different?

Yes, you can:

Ich trinke seit dem neuen Wasserfilter fast nur noch Leitungswasser …

This is also correct. The difference is just emphasis and style:

Seit dem neuen Wasserfilter trinke ich …
→ Emphasizes the time frame: Ever since the new filter…
Ich trinke seit dem neuen Wasserfilter …
→ Starts with ich, more neutral focus on the subject.

Both follow V2 word order; they just choose different elements for the first position.

What is the nuance of fast nur noch in trinke ich fast nur noch Leitungswasser?

Let’s break it down:

nur = only
noch = still / anymore / no longer something else
nur noch → “only (and not anything else anymore)”
- It implies a change: I used to drink other things too, but now I basically only drink this.
fast = almost / nearly

So:

nur Leitungswasser = only tap water
nur noch Leitungswasser = now only tap water (not other drinks anymore)
fast nur noch Leitungswasser = almost only tap water now
→ You drink tap water most of the time, and only rarely something else.

So fast nur noch suggests:

tap water is your main drink,
other options are now quite rare,
and this is a newer situation (since the filter).

Why is there no article before Leitungswasser? Why not das Leitungswasser?

Leitungswasser (tap water) is an uncountable (mass) noun here, used in a general sense:

Ich trinke Leitungswasser. = I drink tap water (in general).

German often leaves out the article with mass nouns used generally:

Ich trinke Kaffee. (coffee)
Er trinkt Bier. (beer)
Wir trinken Wein. (wine)
Sie trinkt Leitungswasser. (tap water)

If you say das Leitungswasser, you usually refer to a specific tap water (for example, the tap water in a particular city or building), not to what you usually drink in general. Here, the sentence is about a general habit, so no article is used.

What does Leitungswasser literally mean, and what gender is it?

Leitungswasser is a compound noun:

die Leitung = pipe, line (here: water pipe)
das Wasser = water

The last part of a German compound decides the gender, so:

das Wasser → das Leitungswasser (neuter)

Literally: “pipe-water”, i.e. water from the mains / tap water.

Why does the second part say und kaufe selten Flaschen instead of und ich kaufe selten Flaschen?

In coordinated clauses with und, German can omit the repeated subject if it’s the same as in the first clause, especially with ich, du, wir, ihr:

Ich trinke Kaffee und (ich) esse Kuchen.
Wir gehen ins Kino und (wir) kaufen Popcorn.

So here:

Full form: … trinke ich fast nur noch Leitungswasser und ich kaufe selten Flaschen.
Natural, shorter form: … trinke ich fast nur noch Leitungswasser und kaufe selten Flaschen.

The subject ich is understood and doesn’t need to be repeated. This is very typical and sounds natural.

If the subject ich is missing in und kaufe selten Flaschen, is the word order still okay? Isn’t the verb supposed to be second?

This is a special case in coordinated clauses.

After und, we have a new main clause, but with the subject elliptically omitted:

Implied structure: (ich) kaufe selten Flaschen.

If we wrote out the pronoun, it would be:

und ich kaufe selten Flaschen → verb-second as usual.

When the pronoun is dropped, the finite verb kaufe ends up as the first overt element, but it is still considered part of a normal main clause structure with an omitted subject. Native speakers accept this easily; it is very natural.

So:

… und kaufe selten Flaschen.
is perfectly fine, because the subject ich is understood from the previous clause.

Why is it selten Flaschen and not Flaschen selten? Where does selten normally go?

Selten is an adverb meaning rarely / seldom. In the most neutral word order, adverbs of frequency like selten, oft, immer usually go before the direct object:

Ich kaufe selten Flaschen. (neutral, very common)
Ich kaufe Flaschen selten. (possible, but puts a bit more emphasis on Flaschen as the thing that rarely happens)

In the given sentence:

… und kaufe selten Flaschen.
follows the neutral pattern: verb – adverb (frequency) – object.

So selten in front of Flaschen is the most typical placement.

What exactly does selten add compared to ich kaufe Flaschen?

ich kaufe Flaschen = I buy bottles (a simple statement of fact)
ich kaufe selten Flaschen = I rarely buy bottles

So selten tells us:

It is not your regular habit.
It happens only from time to time.
Combined with fast nur noch Leitungswasser, it suggests that buying bottled water has become the exception, not the rule.

In kaufe selten Flaschen, what does Flaschen refer to? Why is it just Flaschen and not Wasser in Flaschen?

Here Flaschen is short for something like:

Wasser in Flaschen (water in bottles)
Wasserflaschen (water bottles)
or Flaschenwasser (bottled water, more formal/technical)

German, like English, often omits obvious words when they are clear from context:

Ich esse gern Äpfel und kaufe selten Bananen.
Ich trinke fast nur noch Leitungswasser und kaufe selten Flaschen.
→ Context: clearly means bottled water or at least bottled drinks, not random empty bottles.

So it’s natural to just say Flaschen here. The missing word Wasser is understood from Leitungswasser in the first part.

Why is the present tense trinke ich used with seit? Could it also be a perfect tense like habe ich getrunken?

With seit + a time expression that starts in the past and continues into the present, German very often uses the present tense, not the perfect:

Seit zwei Jahren wohne ich in Berlin.
Seit 2010 arbeite ich hier.
Seit dem neuen Wasserfilter trinke ich fast nur noch Leitungswasser.

All of these describe an action that started in the past and is still true now.

You can see perfect forms with seit in some contexts (especially in southern Germany/Switzerland), but for a current, ongoing habit, the present tense with seit is the standard and safest choice in German.