Sorry, I'm really new to Arduino and electronics, but I need to know: is it okay to connect my 5V, 2.5A power bank to the USB port of my Arduino Mega? By the way, the power bank has 3 USB outputs, each with different amperage: one is 2.5A and the others 1A.
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Welcome to the forum
The Arduino will not care where the 5V comes from as long as it can supply enough current
The current ratings of the powerbank relate to the amount that can be supplied, not the amount that will be supplied. The Arduino will use whatever it needs
So the answer tou your question is yes
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thanks for your time <3, that's helpful
Powerbanks are designed to charge cellphone batteries, and most of them switch-off when current draw falls below a certain threshold (battery fully charged). A Mega, without any sensors/LEDs, draws about 70mA, which might be too low to stop the powerbank from switching off (after some time).
Leo..
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Yes, you may find that using a power bank is an exercise in frustration because of the auto-off design that Leo described. But there are small "UPS" power supplies that usually have an 18650 lithium ion cell, a charger, and a boost converter. They don't shut down automatically. But they may or may not have a USB output port. I haven't seen one yet that has everything right.
Some powerbanks will have a selectable "trickle-mode" which will stay alive with low current draws.
The ones I've seen with trickle charging, such as the Ankers, still shut down after about two hours. They are intended for things like headsets or earbuds or microphones, things that draw very small charge currents. But they still don't want to keep the boost converter running all the time, so they shut down after a time that should be long enough to charge the small devices. I don't know if all of them operate that way, but you just want to investigate any power bank that provides trickle charging to see how long the trickle actually lasts.
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You can solve this by periodically presenting a relatively large load to the power bank.
A '555 timer chip that is configured as an astable oscillator with a short positive pulse to switch on a smallish resistor is one way.
If your loop runs free, and you have an output pin available you can do the same in software, just the same: periodically switch on a large-ish load under program control.
I've used both.
Some need small enough extra current that just placing a permanent load across is not a terrible idea.
a7
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I did the same, MOSFET switching 60mA load in for 20mS every minute for the bank that I was using.
Tom.. 
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