Похоже, в доме нет электричества, поэтому свет не включается.

Похоже here functions as a predicative word (категория состояния), similar to кажется / похоже = it seems / apparently. It’s commonly used in an impersonal way:

• Похоже, ... = It looks like ... / Apparently, ...
  It’s historically related to the short form of the adjective похожий (similar), but in this pattern you can treat it as a fixed “it seems” expression rather than a normal adjective describing a noun.

Because Похоже introduces a parenthetical/introductory comment (вводное слово / вводная конструкция) about the speaker’s assessment. What follows is the main statement. In Russian, introductory words are usually set off by commas:

• Похоже, в доме нет электричества.
  Comparable to English commas in Apparently, there’s no electricity in the house.

You can, but the most natural form is Похоже, что в доме нет электричества (with a comma), or simply Похоже, в доме нет электричества (without что).

• Похоже, что ... is a bit more explicit/structured: It seems that...
• Похоже, ... is more conversational and very common in speech.

Russian expresses there is/are not with нет (the negative form of есть in this meaning). You generally don’t say электричество не есть.
Pattern: (где?) + нет + (чего?)
So: в доме нет электричества = there is no electricity in the house.

After нет, Russian normally uses the genitive to mark “absence”:

• нет (кого? чего?) → genitive
  So электричества is genitive singular of электричество.
  Same idea: нет воды, нет времени, нет людей.

в доме means in the house (inside the building). It’s a location phrase: в + prepositional (в доме).

дома usually means at home (as a general place/state), not specifically inside the building as a location description. You can say:

• Похоже, дома нет электричества = Looks like there’s no electricity at home (more about your household/home situation).
  But в доме is more literal/spatial.

поэтому means therefore / that’s why / so. It links the cause and result: no electricity → the light doesn’t turn on.

Position-wise, поэтому often comes at the start of the second clause, after a comma:

• ..., поэтому свет не включается.
  You could also use alternatives with slightly different style: так что, из‑за этого, по этой причине.

Because the sentence is made of two clauses (a cause and a result) joined in a compound sentence. Russian typically separates such clauses with a comma:

• Похоже, в доме нет электричества, поэтому свет не включается.
  Even though поэтому is not a conjunction like и/но, it still introduces the second clause and is normally preceded by a comma in this structure.

свет in Russian can mean:

• light in general, or
• the lights / the light (fixture) in everyday speech.

In this context, свет не включается is a common way to say the light won’t turn on / the lights won’t come on (often meaning a lamp or the room lights).

включаться is the reflexive/intransitive counterpart of включать/включить:

• Я включаю свет = I turn on the light (someone acts on it)
• Свет включается = The light turns on / comes on (focus on the result/state; no agent mentioned)

не включают would mean they don’t turn it on (implies some people are failing/refusing). Here the point is that the light cannot turn on because there’s no electricity, so не включается is more natural.

Word order: свет не включается is neutral. не включается свет is also possible, often a bit more “event-like” or contrastive.

It’s present tense, imperfective: (он) включается / не включается. Russian present tense often covers “right now” situations, like English present progressive or simple present depending on context:

• Свет не включается = The light isn’t turning on / won’t turn on (when I try)

Using perfective present (future meaning) like не включится would shift toward “it will not turn on (at all / as a result)” and can sound more final or predictive.

Yes, but it changes meaning.

• свет не включается = you try (or could try), but it doesn’t turn on (a problem/process).
• свет не включён = the light is not turned on (a state; it might simply be off, with no implication of malfunction).

So in this sentence (no electricity → unable to turn on), не включается is the better match.