Nel mio zaino tengo una bottiglia d’acqua fresca.

Nel means in the here.

It is a contraction of:

• in = in
• il = the

So:

• nel mio zaino = in + il mio zaino = in my backpack

In Italian, this kind of contraction is very common:

• in + il = nel
• in + la = nella
• in + i = nei
• in + le = nelle

Italian usually keeps the definite article with possessive adjectives such as mio, tuo, suo, etc.

So Italian says:

• il mio zaino = my backpack

not usually:

• mio zaino

When you add in, you get:

• in + il mio zaino → nel mio zaino

As for nello, that would come from in + lo, but with a possessive adjective before the noun, Italian normally uses il, not lo:

• il mio zaino
• not lo mio zaino

So nel mio zaino is correct.

Mio means my, and it agrees with the noun being possessed, not with the owner.

Zaino is:

• masculine
• singular

So the possessive must also be masculine singular:

• mio zaino

Compare:

• il mio zaino = my backpack
• la mia bottiglia = my bottle
• i miei libri = my books
• le mie chiavi = my keys

Italian often drops subject pronouns when the verb ending already shows who the subject is.

Here, tengo already means:

• I keep
• I hold
• I keep with me

So io is not necessary.

You can say Io tengo... if you want extra emphasis, but the normal version is just:

• Tengo una bottiglia d’acqua fresca.

This is very common in Italian:

• Parlo italiano. = I speak Italian.
• Vado a casa. = I’m going home.

Tenere often means to keep, to hold, or to keep/store in a place.

So:

• Nel mio zaino tengo... suggests I keep ... in my backpack or I have ... in my backpack

This is a little more specific than ho, which just means I have.

Compare:

• Ho una bottiglia d’acqua. = I have a bottle of water.
• Tengo una bottiglia d’acqua nello zaino. = I keep/have a bottle of water in my backpack.
• Porto una bottiglia d’acqua. = I’m carrying/bringing a bottle of water.

So tengo focuses on the fact that the bottle is being kept in the backpack.

Because bottiglia is a feminine singular noun.

So the indefinite article is:

• una = a

That gives:

• una bottiglia = a bottle

Compare:

• un libro = a book
• una bottiglia = a bottle
• una casa = a house

D’acqua is just di acqua with elision.

Because acqua starts with a vowel, di often becomes d’:

• di acqua → d’acqua

This is very common and sounds more natural.

Also, after container words like bottiglia, Italian usually uses di without an article:

• una bottiglia d’acqua = a bottle of water
• un bicchiere di vino = a glass of wine
• una tazza di tè = a cup of tea

Dell’acqua would mean something more like some water or of the water, and it is not the normal choice in this phrase.

In normal interpretation, it describes acqua:

• una bottiglia d’acqua fresca = a bottle of cool/fresh water

That is the most natural meaning.

However, grammatically there is a small ambiguity, because both bottiglia and acqua are feminine singular, so fresca could match either one in form.

In practice, context and common sense make acqua fresca the likely meaning.

A useful note: in Italian, acqua fresca usually means cool/fresh water, not freshwater as opposed to salt water. For freshwater in that sense, Italian usually says acqua dolce.

Because in Italian, descriptive adjectives often come after the noun.

So:

• acqua fresca
• vino rosso
• una casa grande

This is more normal than putting the adjective before the noun.

Sometimes Italian adjectives can go before the noun, but that often changes the tone, emphasis, or style. In this sentence, acqua fresca is the standard, natural order.

Yes.

You could also say:

• Tengo una bottiglia d’acqua fresca nel mio zaino.

That has basically the same meaning.

The version with Nel mio zaino at the beginning gives a little more emphasis to the location:

• Nel mio zaino tengo... = In my backpack, I keep...

So the original sentence sounds a bit like the speaker is highlighting where the bottle is. Both orders are correct and natural.