Learn Hardcore Italian: Nel frigorifero tengo l’anguria per la merenda di domani. - I keep the watermelon in the fridge for tomorrow’s snack.

nel is the contraction of the preposition in + the definite article il, so nel frigorifero literally means in the refrigerator. In Italian, certain prepositions merge with the masculine singular definite article:

in + il → nel
a + il → al
di + il → del
su + il → sul

What does tengo mean here, and what is its infinitive form?

tengo is the first-person singular present indicative of the verb tenere, which means to keep, to hold, or to store. In this sentence, tengo translates as “I keep” (i.e. “I store”).

Why is there an apostrophe in l’anguria, and could I say la anguria instead?

The apostrophe marks an elision: the vowel a in la (the feminine singular article) is dropped before another vowel. So:

la + anguria → l’anguria
You cannot say la anguria in standard Italian; you must use l’anguria to avoid a vowel clash.

Why use the definite article with anguria? Could I say una anguria instead?

Using l’anguria (the watermelon) signals you’re talking about a specific watermelon you have in mind. If you said una anguria, you’d be introducing a watermelon for the first time (a watermelon, not necessarily the one you mean). Here, the speaker refers to the watermelon already known in the context.

What does merenda mean, and is it the same as the English word “snack”?

merenda is a light meal or snack typically eaten in the mid-afternoon (especially by children, but adults use it too). It’s very close to the English “snack”, but carries the idea of a small meal between lunch and dinner.

Why is it per la merenda di domani rather than just per domani or per la merenda domani?

per indicates purpose (“for”).
la merenda names the thing you’re preparing for.
di domani is a typical Italian way to say “tomorrow’s” (literally “of tomorrow”), so merenda di domani = tomorrow’s snack.
Dropping di (as in per la merenda domani) would sound ungrammatical: Italian needs di to link the noun and the time expression when expressing possession or attribution.

Could I use mettere instead of tenere, as in Metto l’anguria nel frigorifero?

Yes, you could say Metto l’anguria nel frigorifero (“I put the watermelon in the fridge”). The nuance is:

mettere emphasizes the action of placing something.
tenere emphasizes keeping it there or storing it.
Both are correct; you choose based on whether you want to stress the act of putting it away (mettere) or the fact that you’re keeping it stored there (tenere).

Can I change the word order, for example:
“Tengo l’anguria nel frigorifero per la merenda di domani”?

Absolutely. Italian word order is flexible. Your version is perfectly natural:
“Tengo l’anguria nel frigorifero per la merenda di domani.”
The original fronted nel frigorifero simply shifts emphasis onto where it’s stored, but meaning stays the same.