Dodavatel pošle účet a já budu šetřit elektřinu.

Because pošle is from a perfective verb: poslat.

In Czech, the present forms of perfective verbs usually refer to the future, not the present. So:

• pošle = he/she/it will send
• not he/she/it sends in a general present sense

Compare:

• posílá = he/she sends / is sending
  
  • this is the imperfective verb posílat
• pošle = he/she will send
  
  • this is the perfective verb poslat

So Dodavatel pošle účet means the supplier will send the bill as a single completed future action.

Because šetřit is an imperfective verb.

In Czech, the future of most imperfective verbs is formed with:

• future of být
  • infinitive

So:

• budu šetřit = I will save / I will be conserving

This is different from pošle, where the verb is perfective and already has a built-in future meaning.

A useful contrast:

• budu šetřit elektřinu = I will be trying to save electricity / I will conserve electricity
• a perfective form would sound more like achieving a result, not the ongoing activity

So this sentence uses two different future patterns because the two verbs have different aspect.

They show the two main Czech aspects:

• pošle = perfective
• budu šetřit = imperfective

Perfective usually presents an action as a whole, as a completed event:

• Dodavatel pošle účet
  The supplier will send the bill.

Imperfective focuses more on process, duration, repetition, or general activity:

• já budu šetřit elektřinu
  I will be saving electricity / trying to use less electricity

So the sentence feels very natural:

• one future event: the supplier will send the bill
• one ongoing future behavior: I will conserve electricity

That is true: Czech often leaves out subject pronouns because the verb ending already shows the person.

So you could also say:

• Dodavatel pošle účet a budu šetřit elektřinu.

That would still be correct.

Here, já is included for emphasis or contrast. It gives a feeling like:

• and I will save electricity
• or even and as for me, I’ll save electricity

So já is not required for grammar, but it helps highlight the second subject.

Because elektřinu is in the accusative case, which is used here for the direct object of šetřit.

The basic form is:

• elektřina = electricity

But after the verb šetřit in this sentence, it becomes:

• šetřit elektřinu = to save / conserve electricity

This is a normal pattern for a feminine noun ending in -a:

• nominative singular: elektřina
• accusative singular: elektřinu

So the ending changes because the noun is receiving the action.

Because účet is a masculine inanimate noun, and in the singular its accusative form is the same as its nominative form.

So:

• nominative: účet
• accusative: účet

That is why:

• Dodavatel pošle účet

has účet unchanged, even though it is the direct object.

This is very common with masculine inanimate nouns in Czech.

Yes, here a simply means and.

It connects the two clauses:

• Dodavatel pošle účet
• a já budu šetřit elektřinu

Because já is explicitly stated, the sentence can also carry a slight sense of contrast or balance:

• The supplier will send the bill, and I will save electricity

But the core meaning of a here is just the normal conjunction and.

No, Czech word order is fairly flexible.

The sentence as given is the most neutral, straightforward order:

• Dodavatel pošle účet a já budu šetřit elektřinu.

But other orders are possible if you want different emphasis. For example:

• Účet pošle dodavatel a já budu šetřit elektřinu.
  Emphasis on the bill
• Dodavatel pošle účet a elektřinu budu šetřit já.
  Emphasis on I or electricity

Even though the word order can change, the cases help show who is doing what.

So for a learner, the given version is a good default pattern:

• subject + verb + object

The main special letters here are:

• š = like sh in shop
• č = like ch in church
• ř = a special Czech sound with an r
  • zh/sh quality; English does not have an exact equivalent

A rough guide to some words:

• pošle ≈ posh-leh
• účet ≈ oo-chet
• šetřit ≈ roughly shet-rzhit
  but ř takes practice
• elektřinu ≈ e-lek-rzhi-nu very roughly

Also, Czech stress normally falls on the first syllable of the word:

• DOdavatel
• POšle
• Účet
• BUdu
• ŠEtřit
• Elektřinu

So even in a longer word like elektřinu, the stress is still on the first syllable.