Eu ainda não paguei o aluguel, mas vou pagar pelo aplicativo agora.

Yes, you can often omit it. Portuguese verb endings usually show the subject, so Ainda não paguei o aluguel... is natural and common.
Keeping Eu can add emphasis/contrast (e.g., I haven’t paid, maybe someone else has).

Ainda não means not yet: the action hasn’t happened up to now, but it’s expected to happen.
Não is just not and doesn’t include that “up to now / expected later” nuance.

Portuguese commonly uses the pretérito perfeito (paguei) to talk about a completed action that didn’t happen in the relevant time frame: I didn’t pay (it).
With ainda não, it becomes “I haven’t paid it yet.” This is a very typical way to express what English often puts in the present perfect.

Paguei is the pretérito perfeito and can match either English I paid or I have paid, depending on context.
In this sentence, with ainda não, it functions like I haven’t paid yet.

Portuguese often uses definite articles more than English does. Pagar o aluguel is the normal way to say pay the rent (the specific rent you owe).
You might omit the article in some contexts (especially in signs/headlines), but in everyday speech o aluguel sounds most natural.

In Brazil, aluguel is the standard word for rent (especially rent you pay for a place).
Renda usually means income/earnings. (In some other Portuguese varieties, renda can mean rent, but in Brazil that’s not the default.)

Mas = but. It contrasts two clauses: not paid yet vs. will pay now.
The comma before mas is standard in writing when it links two independent clauses: ..., mas ....

Both. Vou pagar (literally “I’m going to pay”) is the common spoken way to express a near/planned future and intention.
It can sound more immediate than the simple future pagarei.

Yes, but it sounds more formal or written, and sometimes more “firm/official.”
In casual Brazilian Portuguese, vou pagar is usually more natural.

Pelo = por + o and here por means via / by means of: pay via the app.
No aplicativo (em + o) means in/on the app (location/context), which can also be possible, but it slightly shifts the idea to where the action happens rather than the method. Pelo aplicativo strongly emphasizes the method/channel.

It’s a contraction: por + o = pelo.
Similarly: por + a = pela, por + os = pelos, por + as = pelas.

Agora is flexible. The sentence’s placement (...agora) is very natural and emphasizes “right now.”
You could also say: ...mas agora vou pagar pelo aplicativo. That puts extra focus on agora (now, as opposed to earlier).