Na té stěně není žádná zásuvka, proto tam lampa nemůže být.

Here zásuvka means an electrical socket / outlet.

A useful warning: zásuvka can also mean drawer in other contexts. Czech uses the same word for both, so the context decides:

• elektrická zásuvka = electrical outlet
• zásuvka ve stole = drawer in a desk

In this sentence, because of lampa and the idea that it cannot be there, it clearly means outlet.

Because Czech uses na + the locative case to express being on a surface or at a location.

• na stěně = on the wall
• na stole = on the table
• na obrázku = in/on the picture

Here the phrase describes location, not movement. So Czech uses the locative:

• base form: ta stěna
• locative: na té stěně

A very common contrast is:

• na té stěně = on that wall
• na tu stěnu = onto that wall

So:

• locative = location
• accusative = motion toward a place

Because both words have to change to the locative singular, and they must agree with each other.

• ta → té
• stěna → stěně

So:

• nominative: ta stěna = that wall
• locative: na té stěně = on that wall

This is normal adjective/demonstrative agreement in Czech: the demonstrative and the noun match in gender, number, and case.

Because Czech has no articles.

English needs words like a, an, and the, but Czech does not. Whether something is definite or indefinite is usually understood from:

• context
• word order
• demonstratives like ten, ta, to
• the general situation

So lampa can mean a lamp or the lamp, depending on context. In this sentence, English would often translate it as the lamp, because it sounds like a specific lamp is being discussed.

Žádná means no / not any and makes the absence stronger and more explicit.

• Na té stěně není zásuvka. = There isn’t an outlet on that wall.
• Na té stěně není žádná zásuvka. = There is no outlet at all on that wall.

Both are possible, but žádná is very natural when you want to stress that none exists there.

It agrees with zásuvka:

• žádná = feminine singular nominative
• because zásuvka is feminine singular nominative

Because in this sentence zásuvka is the grammatical subject of není.

The structure is basically:

• there is no socket
• Czech: není žádná zásuvka

With být in this kind of existence sentence, the thing that exists or does not exist is in the nominative:

• Je tam zásuvka. = There is an outlet there.
• Není tam zásuvka. = There isn’t an outlet there.
• Není tam žádná zásuvka. = There isn’t any outlet there.

By contrast, after a verb that takes a direct object, you would use the accusative:

• Nevidím zásuvku. = I don’t see an outlet.

So here:

• žádná zásuvka = nominative
• žádnou zásuvku would be accusative, which would not fit this sentence

Proto here means therefore, that’s why, or for that reason.

It introduces the result of the first clause:

• Na té stěně není žádná zásuvka = There is no outlet on that wall
• proto tam lampa nemůže být = therefore the lamp cannot be there

The comma is used because there are two clauses:

• není
• nemůže být

So the sentence is divided naturally into:

1. the reason
2. the consequence

A natural English equivalent would be:

• There’s no outlet on that wall, so the lamp can’t be there.

Tam means there, and it refers back to na té stěně.

Czech often repeats a location like this instead of leaving it completely implicit. It makes the second clause sound more natural and complete:

• Na té stěně není žádná zásuvka, proto tam lampa nemůže být.

Without tam, the sentence would still be understandable, but it would sound less smooth:

• Na té stěně není žádná zásuvka, proto lampa nemůže být.

That version feels incomplete unless the location is very strongly understood from context.

So tam is doing useful work: it clearly means there/on that wall.

Because nemůže být means cannot be, not simply is not.

The speaker is making a logical conclusion:

• there is no outlet on that wall
• therefore the lamp cannot be there

So this is about impossibility or practical impossibility, not just a plain statement of fact.

Compare:

• Lampa tam není. = The lamp is not there.
• Lampa tam nemůže být. = The lamp cannot be there.

The second one is more like It can’t be there, often because of some reason just given.

This is an important difference:

• nemůže být = cannot be / it is not possible
• nesmí být = must not be / it is not allowed

In this sentence, the problem is the lack of an outlet, so it is about possibility, not permission.

So:

• Lampa tam nemůže být. = The lamp can’t be there.
• Lampa tam nesmí být. = The lamp mustn’t be there.

The second one would suggest a rule, order, or prohibition.

Yes. Czech word order is flexible, and changing it changes the emphasis more than the basic meaning.

For example:

• Proto tam lampa nemůže být. = neutral, natural
• Proto lampa tam nemůže být. = possible, slightly different focus
• Lampa tam proto nemůže být. = puts more attention on the lamp
• Tam lampa nemůže být. = emphasizes there

In your original sentence, tam lampa nemůže být sounds natural because the place is the important point: there/on that wall.

So the meaning stays similar, but the information focus shifts depending on word order.