Tato zásuvka už funguje, takže lampa u stolu může být tady.

Because zásuvka is a feminine singular noun in the nominative case, and the demonstrative has to match it.

• tento = masculine
• tato = feminine
• toto = neuter

So:

• tato zásuvka = this socket/outlet

This is normal agreement in Czech: the word for this changes according to gender, number, and case.

No. Zásuvka can mean both:

• drawer
• electrical socket / outlet

The context tells you which meaning is intended.
Here, because the sentence talks about a lamp and something functioning, electrical socket/outlet is the natural meaning.

Už usually means already or sometimes now in the sense of at this point.

So:

• Tato zásuvka už funguje = This outlet already works / This outlet is working now

It suggests a change from an earlier situation:

• before: it did not work
• now: it works

Funguje is the 3rd person singular present form of fungovat.

• fungovat = to function, to work
• funguje = it works / it is functioning

Since the subject is tato zásuvka (this outlet), Czech uses the singular verb form:

• zásuvka funguje = the outlet works

Czech often uses fungovat for machines, devices, systems, plans, methods, etc.

Because takže introduces a result or consequence, like so or therefore in English.

• Tato zásuvka už funguje, takže...
• This outlet works now, so...

In Czech, this kind of clause is normally separated by a comma.

Takže means so, therefore, which means that, or as a result.

It connects the first part of the sentence with the consequence in the second part:

• The outlet works now, so the lamp can be here.

It is very common in everyday Czech.

Because the preposition u takes the genitive case.

• stůl = table
• u stolu = by the table / at the table / near the table

So stolu is the genitive singular form of stůl.

This is something you just have to learn with the preposition:

• u + genitive

Examples:

• u domu = by the house
• u školy = by the school
• u stolu = by the table

It can mean either, depending on context. The core idea is near / at / by.

With lampa u stolu, English will often translate it as:

• the lamp by the table
• the lamp at the table

The exact English wording depends on the situation, but the Czech phrase itself is normal.

Because může is a modal verb and it is followed by the infinitive.

• moci = can / to be able to
• může = can
• být = be / to be

So:

• může být = can be

This is the standard pattern in Czech:

• může přijít = he/she can come
• může stát = it can stand
• může být tady = it can be here

It can potentially mean either possibility or permission, just like English can.

Here, the most natural interpretation is probably possibility / suitability:

• the lamp can be here
• meaning: it is possible / okay / workable for the lamp to be here

The exact nuance depends on context.

Because tady refers to location, while sem refers to motion toward here.

• tady = here
• sem = to here / hither

So:

• Lampa může být tady = The lamp can be here
  (location)

But:

• Dej lampu sem = Put the lamp here
  (movement toward this place)

This is a very important Czech distinction.

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

This sentence could be rearranged in different ways depending on emphasis, for example:

• Tato zásuvka už funguje, takže lampa může být tady.
• Tato zásuvka už funguje, takže může být lampa tady.
• Tato zásuvka už funguje, takže tady může být lampa.

Not all versions sound equally natural in every context, but Czech often moves words around to change focus or emphasis, not basic meaning.

The original sentence is perfectly understandable, but the exact word order helps highlight what is new or important.

Because Czech has no articles.

English needs:

• the outlet
• a lamp

Czech simply says:

• zásuvka
• lampa

Definiteness is understood from context, word order, or demonstratives like tato (this).

So tato zásuvka already makes the reference specific without needing a separate word for the.