Když skončím práci, vždycky vypnu počítač i lampu v kanceláři.

Literally, když means when. In this sentence, though, because of vždycky (always), the whole idea is whenever / every time:

Když skončím práci, vždycky...
= When/Whenever I finish work, I always...

So když itself is still when, but the full sentence has a repeated, habitual meaning.

Because both verbs are perfective:

• skončit = to finish, to bring to an end
• vypnout = to switch off, turn off completely

In Czech, the present form of a perfective verb usually has future meaning. So:

• skončím = I will finish
• vypnu = I will switch off

In this sentence, Czech is describing a repeated sequence of completed actions:

When I finish work, I always switch off the computer and the lamp.

So even though the forms look like present tense, they naturally refer to the completion of future actions in each repeated situation.

Because práce is a feminine noun, and here it is the direct object of skončím.

The verb skončit in this use takes the accusative case, so:

• nominative: práce
• accusative: práci

So:

• skončím práci = I finish the work / I finish work

That is why the ending changes.

Not exactly.

• skončit práci = to finish the work / complete the work
• skončit s prací = to finish with work / stop working / be done working

In many everyday situations, they can be close in meaning, but there is a nuance:

• skončit práci focuses more on the work as a task being completed
• skončit s prací focuses more on being done with working

In your sentence, skončím práci is completely natural.

Both nouns are in the accusative, because they are both objects of vypnu.

But they change differently:

• lampa is feminine:

  • nominative: lampa
  • accusative: lampu

• počítač is masculine inanimate:

  • nominative: počítač
  • accusative: počítač

So počítač looks the same in nominative and accusative, while lampa changes to lampu.

Here i means something like also / too / as well / and also.

So:

počítač i lampu
= the computer and the lamp too

It links the second item and emphasizes that it is included as well.

A rough comparison:

• počítač a lampu = the computer and the lamp
• počítač i lampu = the computer and the lamp too / the computer as well as the lamp

In this sentence, i sounds very natural.

It comes from the infinitive vypnout.

Some Czech verbs in -nout form the 1st person singular like this:

• vypnout → vypnu
• zapnout → zapnu
• sednout → sednu

So vypnu means I switch off / I will switch off.

This is just a normal conjugation pattern, even though it may look surprising at first.

Because Když skončím práci is a subordinate clause, and Czech normally separates subordinate clauses with commas.

So the structure is:

• Když skončím práci, = subordinate clause
• vždycky vypnu počítač i lampu v kanceláři. = main clause

In Czech punctuation, that comma is required.

This is a good question, because it can feel slightly ambiguous.

Since v kanceláři comes right after lampu, many learners will first read it as:

• the lamp in the office

So:

vypnu počítač i lampu v kanceláři
can sound like
I turn off the computer and the lamp in the office

In real context, it may also simply describe where the action happens. Czech often leaves this kind of thing to context.

If you wanted to make the location of the whole action clearer, you could move it:

• Když skončím práci, vždycky v kanceláři vypnu počítač i lampu.

That more clearly suggests In the office, I always switch off the computer and the lamp.

Yes, Czech word order is fairly flexible, and vždycky can move, but the placement changes the emphasis a little.

Your sentence:

Když skončím práci, vždycky vypnu počítač i lampu v kanceláři.

This sounds natural and makes always apply to the whole main action.

You could also say:

Vždycky, když skončím práci, vypnu počítač i lampu v kanceláři.

That puts stronger emphasis on every time.

So the original word order is normal, but not the only possible one.

Because vypnout is perfective, and it presents the action as a complete result: the computer and lamp end up switched off.

• vypnu = I switch off / I will switch off completely
• vypínám = I switch off / I am switching off, with an imperfective, habitual or ongoing feel

With vždycky, both can make sense in some contexts, but they are not quite the same:

• vždycky vypnu = every time, I perform the complete action
• vždycky vypínám = I have the habit of switching off

In this sentence, vypnu is very natural because switching something off is a single completed action.

Yes, but the meaning would be less explicitly habitual.

• Když skončím práci, vypnu počítač i lampu v kanceláři.

This could mean:

• When I finish work, I switch off the computer and the lamp in the office
• or, depending on context, When I finish work, I’ll switch off the computer and the lamp in the office

Adding vždycky makes it clearly mean a repeated routine:

• Whenever I finish work, I always switch off...

So vždycky is there to make the habitual meaning unmistakable.

Yes, you could, but the nuance is slightly different.

• Když skončím práci = when I finish the work / when I am done working
• Po práci = after work

Po práci is shorter and often sounds more general, like after work as a time period.
Když skončím práci focuses more on the moment the work is finished.

So both are possible, but your original sentence is a bit more event-based: first I finish work, then I switch things off.