Se vuoi, facciamo due passi lungo il fiume.

Yes. Se vuoi literally means if you want or if you’d like.

In this sentence, it sounds natural and polite, like:

• If you want, ...
• If you’d like, ...
• If you feel like it, ...

Italian often uses se vuoi to soften a suggestion, just like English does.

Facciamo is the 1st person plural present indicative of fare: we do / we make.

But in Italian, this form is also very commonly used to make a suggestion:

• Facciamo una pausa. = Let’s take a break.
• Andiamo? = Shall we go?
• Mangiamo fuori. = Let’s eat out.

So here facciamo due passi means let’s go for a walk, not literally we do two steps.

It is similar to English using Let’s ...

Because Italian usually expresses let’s with the 1st person plural verb form.

So:

• Facciamo = we do / let’s do
• Andiamo = we go / let’s go
• Prendiamo un caffè = let’s have a coffee

Italian does have ways to make suggestions more explicitly, but the simple noi form of the verb is the normal everyday way.

Literally, yes: due passi = two steps.

But very often it is an idiomatic expression meaning:

• a short walk
• a little walk
• a stroll

So fare due passi is a very common expression meaning to go for a short walk.

Other similar expressions:

• fare una passeggiata = to go for a walk
• andare a fare due passi = to go take a short walk

Italian can use a verb meaning walk, such as camminare, but fare due passi is a very natural everyday expression.

Compare:

• Camminiamo lungo il fiume. = Let’s walk along the river.
• Facciamo due passi lungo il fiume. = Let’s take a little walk along the river.

The second one often sounds a bit lighter, more casual, and more like a pleasant suggestion.

Yes. Here lungo means along, and it functions as a preposition.

So:

• lungo il fiume = along the river

You may also see:

• lungo la strada = along the road
• lungo il mare = along the sea

Be careful: lungo can also be an adjective meaning long, but in this sentence it clearly means along.

Because Italian uses definite articles much more often than English.

So where English says:

• along the river

Italian says:

• lungo il fiume

Even when English might omit an article in some contexts, Italian often keeps it.

Because Italian usually leaves subject pronouns out when the verb ending already makes the subject clear.

Here:

• vuoi already tells you the subject is tu
• facciamo already tells you the subject is noi

So:

• Se vuoi, facciamo due passi...

is more natural than:

• Se tu vuoi, noi facciamo due passi...

The pronouns can be added for emphasis, but they are normally unnecessary.

Because this is a straightforward real condition: if you want.

So Italian uses the present indicative:

• Se vuoi, ...

This is normal for likely or real conditions in the present.

For example:

• Se hai tempo, vieni con noi. = If you have time, come with us.

The subjunctive is not used here.

The comma separates the introductory conditional phrase from the main clause:

• Se vuoi, = If you want,
• facciamo due passi lungo il fiume.

It works very much like English punctuation in:

• If you want, let’s take a walk along the river.

In short sentences, punctuation can vary a little, but the comma is very natural here.

Yes, depending on context.

Although the literal structure is closer to:

• If you want, let’s take a walk along the river

the overall feeling can also be:

• If you’d like, shall we take a walk along the river?
• We could take a walk along the river, if you want

Italian often uses the present tense in a flexible way for invitations and suggestions.

Yes, vuoi is informal singular, used with tu.

For a formal singular you, you would say:

• Se vuole, facciamo due passi lungo il fiume.

Here vuole goes with formal Lei.

If you are talking to more than one person:

• Se volete, facciamo due passi lungo il fiume.

So:

• vuoi = informal singular
• vuole = formal singular
• volete = plural

Yes, absolutely.

Both are natural:

• Se vuoi, facciamo due passi lungo il fiume.
• Se vuoi, andiamo a fare due passi lungo il fiume.

The version with facciamo is a bit more compact and direct. The version with andiamo a fare emphasizes the idea of going to take a walk.

Both are common, and neither sounds strange.