P.S. HDMI ports on computers are not normally for receiving signals, only for sending.
(If you have the RPi set up for it, you should be able to access it via a cat5 cable.)
That sounds about right. The red LED is power and should be on all the time, the green LED is Activity and should blink with activity (should be configurable within the OS).
How are you connecting those cables and what are you expecting to see? The Pi is a small computer so think of it as any normal computer when you connect it up.
The red LED flashing can be a sign of trying to boot a 3B+ with an SDCard that isn't 3B+ ready.
What in the original post makes you think the power supply is inadequate, or that the red LED is flashing?Your 5v power supply may not be supplying the correct power for the RPi - recommend using the official power supply.