Zaštitićemo fotelju bez obzira na kišu.

Both patterns exist.

Serbian future I is built with the auxiliary hteti in its short form plus the infinitive:

• Mi ćemo zaštititi fotelju.
• Zaštitićemo fotelju.

These mean the same thing.

When the infinitive comes before the auxiliary, verbs ending in -ti usually drop that -ti and join with the clitic:

• zaštititi + ćemo → zaštitićemo

So the sentence is using the attached future form, which is completely normal.

It is:

• 1st person plural: we
• future tense: will
• from the verb zaštititi: to protect

So zaštitićemo means we will protect.

The ending -ćemo tells you the subject is we, so Serbian does not need the pronoun mi unless you want emphasis.

This is about aspect, which is very important in Serbian.

• zaštititi is perfective: to protect successfully, to make safe, to complete the action
• štititi is imperfective: to be protecting, to protect in an ongoing or repeated way

In this sentence, the idea is a single completed future result: we will protect the armchair. That is why zaštititi is the natural choice.

If you used štititi, the meaning would sound more ongoing or habitual, like we will be protecting or we will protect regularly/in general.

Because fotelju is the accusative singular form.

The noun fotelja is feminine and ends in -a. In Serbian, feminine nouns of this type usually change:

• nominative: fotelja
• accusative: fotelju

Here, fotelju is the direct object of the verb zaštitićemo. In English, we do not usually change the noun form, but Serbian does.

Fotelja usually means an armchair or easy chair rather than just any chair.

So it suggests a larger, more comfortable chair, often upholstered, not a simple dining chair. That is why translating it as armchair is often better than just chair.

Yes, bez obzira na is a very common fixed expression.

It means:

• regardless of
• irrespective of
• often also despite

Literally, it is something like without regard to.

So bez obzira na kišu means regardless of the rain or despite the rain.

For the same reason as fotelju: it is in the accusative singular.

The expression bez obzira na is followed by the accusative. So:

• nominative: kiša
• accusative: kišu

That is why the sentence has na kišu, not na kiša.

No. Serbian often leaves subject pronouns out because the verb ending already shows the person and number.

So:

• Zaštitićemo fotelju... = We will protect the armchair...
• Mi ćemo zaštititi fotelju... = also We will protect the armchair...

Adding mi usually gives emphasis, like we in contrast to someone else.

Yes. Serbian word order is more flexible than English word order.

This sentence is neutral and natural:

• Zaštitićemo fotelju bez obzira na kišu.

But you could also say:

• Fotelju ćemo zaštititi bez obzira na kišu.
  This puts more focus on the armchair.
• Bez obzira na kišu, zaštitićemo fotelju.
  This highlights the rain / the circumstance first.

The basic meaning stays the same, but the emphasis changes.

A rough English-friendly guide is:

za-šti-ti-će-mo

Sound by sound:

• ž / z here is plain z
• š = sh
• ti
• ć = a very soft ch-like sound
• e
• mo

A rough approximation is zah-shti-ti-cheh-mo, but remember that ć is softer than English ch.

A rough guide is:

fo-telj-u

The tricky part is lj, which is a single Serbian sound. For an English speaker, it is often easiest to approximate it as ly.

So fotelju can be approximated as fo-TEL-yoo.

That is not perfect, but it is a good learner-friendly approximation.

Yes. A common alternative is uprkos kiši, which also means despite the rain.

So you could say:

• Zaštitićemo fotelju uprkos kiši.

Both are natural, but there is a slight difference in feel:

• bez obzira na kišu = regardless of the rain
• uprkos kiši = despite the rain

The first can sound a little more like the rain will not affect our decision. The second can sound a little more directly concessive: even though it is raining.