Learn Hardcore Russian: Кажется, протечка появилась снова, поэтому я оставлю заявку диспетчеру. - It seems the leak has appeared again, so I will submit a service request to the dispatcher.

Кажется means it seems / apparently and signals that the speaker is not 100% sure, based on impressions or indirect evidence.
It’s close to я думаю (I think), but я думаю sounds more like an opinion or considered thought, while кажется is more like “from what I can tell.”

Why is it Кажется, протечка появилась снова and not Мне кажется, что…?

Both are correct:

Кажется, … = a short, neutral, conversational way to say It seems that…
Мне кажется, что … = more explicit: It seems to me that… (slightly more personal/emphatic)

In everyday speech, dropping мне and что is very common.

What exactly is протечка? Is it “a leak” or “a leakage”?

Протечка usually means a leak in the sense of a specific problem: water leaking from a pipe, ceiling, roof, etc.
It often refers to the incident/problem (“there’s a leak again”) rather than the general phenomenon leakage.

Why does Russian use появилась (“appeared”) for a leak?

Russian commonly uses появиться (to appear/show up) for problems that start or reoccur:

протечка появилась = “a leak showed up / started” It’s a natural way to say the problem has (re)emerged.

Why is появилась feminine?

Because протечка is a feminine noun (it ends in -а). Past tense verbs agree in gender and number:

протечка появилась (feminine singular) Compare:
шум появился (masculine)
пятно появилось (neuter)
проблемы появились (plural)

What does снова mean, and where can it go in the sentence?

снова means again.
It’s flexible in placement, with small nuance shifts:

протечка появилась снова = the leak reappeared again (neutral)
снова появилась протечка = emphasizes “again” a bit more (again, a leak appeared)
протечка снова появилась = also fine, slightly more emphasis on “again”

What does поэтому mean, and how is it different from потому что?

поэтому = therefore / so / that’s why (introduces a result)
потому что = because (introduces a reason)

Here:
Кажется, протечка появилась снова, поэтому… = “It seems the leak is back again, so …”

Why is it я оставлю and not я оставляю?

я оставлю is perfective future (from оставить) and means a one-time, completed action: I will submit / I’ll leave (a request).
я оставляю is imperfective present and would mean something like:

“I am leaving/submitting (it now)” (process-focused), or
“I (generally) submit…” (habit)

In this context, the speaker is deciding to do it as a single action → оставлю fits best.

What does оставлю заявку mean in real-life terms?

оставить заявку is a common set phrase meaning to file/submit a request, especially in housing/services/maintenance contexts.
It can mean:

calling a service and having them log a ticket
submitting a maintenance request
leaving a request with a person responsible

It’s not literally “leave it behind” as in physically abandoning it.

Why is it заявку диспетчеру (dative case)? What’s the implied preposition?

диспетчеру is dative because the structure is essentially:

оставить (что?) заявку (кому?) диспетчеру = “to leave/submit a request to the dispatcher”

Russian often expresses “to someone” with just the dative case, without a preposition.

Who is диспетчер in this context?

In many Russian apartment/building/service systems, диспетчер is the person who receives calls/requests and dispatches workers (plumber, maintenance, аварийная служба, etc.).
In English you might say dispatcher, service operator, maintenance desk, or front desk, depending on the system.

Could the sentence use оформлю заявку or подам заявку instead of оставлю заявку?

Yes, with slightly different tone:

оставлю заявку = very common, neutral, conversational
подам заявку = “I will submit an application/request” (a bit more formal)
оформлю заявку = “I’ll fill out/process the request” (emphasizes formally creating it in the system)

All can work; оставлю заявку sounds especially natural for calling a dispatcher.