Elektristo komencos labori, kondiĉe ke inspektoro akceptos la projekton.

Because after komenci (to begin), the next verb stays in the infinitive.

• komencos = will begin
• labori = to work

So komencos labori means will begin to work.

This is the same pattern as:

• volas helpi = wants to help
• povas veni = can come
• devas atendi = must wait

Only the first verb is conjugated for tense here.

Esperanto handles this more logically than English does. If the accepting happens in the future, Esperanto normally uses the future tense:

• akceptos = will accept

English often uses a present form after if, when, provided that, and similar words even when the meaning is future. Esperanto does not have to do that. So in this sentence, akceptos is perfectly natural because the inspector’s acceptance is a future event.

kondiĉe ke means provided that, on condition that, or as long as.

It introduces a condition that must be met before the main action happens.

So:

• Elektristo komencos labori = The electrician will begin working
• kondiĉe ke inspektoro akceptos la projekton = provided that the inspector approves the project

The whole sentence means that the electrician’s work depends on that approval.

The -n marks the direct object.

Here, the thing being accepted is the project, so projekto becomes projekton.

• inspektoro akceptos la projekton
• the inspector will accept the project

This -n ending is one of the most important features of Esperanto grammar.

Without la, those nouns are indefinite:

• elektristo = an electrician / the electrician, depending on context
• inspektoro = an inspector / the inspector, depending on context

Esperanto has la for a definite noun, but it has no separate word for a/an.

So this sentence is not especially stressing that these are already identified individuals. If you wanted to make them clearly specific, you could say:

• La elektristo komencos labori, kondiĉe ke la inspektoro akceptos la projekton.

Because the speaker apparently has a specific project in mind.

• la projekton = the project

This suggests that the project is already known from the situation or earlier context.

So the sentence treats the project as specific, while electrician and inspector are left more general or are simply not being emphasized as specifically identified.

Yes, but the nuance changes a little.

• se = if
• kondiĉe ke = provided that / on condition that

So:

• Se inspektoro akceptos la projekton... = If the inspector approves the project...
• Kondiĉe ke inspektoro akceptos la projekton... = Provided that the inspector approves the project...

kondiĉe ke sounds a bit more formal and a bit stronger, as if this is an explicit requirement.

Not completely. Esperanto word order is fairly flexible, though the basic order is usually subject–verb–object.

This sentence uses a very natural order:

• Elektristo komencos labori
• inspektoro akceptos la projekton

You could also put the condition first:

• Kondiĉe ke inspektoro akceptos la projekton, elektristo komencos labori.

That means the same thing. The -n on projekton helps show what the object is, so Esperanto does not depend on word order as much as English does.

This sentence is a nice example of common Esperanto endings:

• -o = noun
  
  • elektristo, inspektoro, projekto
• -os = future tense
  
  • komencos, akceptos
• -i = infinitive
  
  • labori
• -e = adverb
  
  • kondiĉe
• -n = direct object marker
  
  • projekton

Seeing these endings clearly is one of the keys to reading Esperanto easily.

Because kondiĉe ke inspektoro akceptos la projekton is a subordinate clause.

In Esperanto, commas are commonly used to separate subordinate clauses from the main clause, especially when the sentence becomes easier to read that way.

So the comma here helps mark the structure:

• main clause: Elektristo komencos labori
• subordinate condition clause: kondiĉe ke inspektoro akceptos la projekton

Yes. -ist- is a common Esperanto suffix meaning a person professionally involved in something, or a habitual practitioner.

So:

• elektr- = electric-
• -ist- = professional/person engaged in
• -o = noun

That gives elektristo = electrician.

You see the same suffix in words like:

• pianisto = pianist
• dentisto = dentist
• ĵurnalisto = journalist