They're an indicator of signal strength. One dot versus 5 dots has got to be some kind of indication...
It is, but it's not a very accurate one. No standard exists for what signal bars mean, and 4 bars on one brand of phone could correspond to something very different on a different phone.
The only way to know for sure would be to put the iPhone in field service mode, do the equivalent on the M8, and get the dB signal readings to compare.
Like I said, my partner's M8 has much faster download speeds in our home than my 6S+ and on the same network. I have two dots and she has four bars. The data speeds kinda correspond with the speed differences we see.
Correlation isn't causation, and it's possible the M8 uses different hardware that quite simply allows for faster throughput. making it universally faster in both good and bad signal conditions. The bars, again, may not be telling the whole story. The way to know for sure is to get the numeric signal strength readings, and to camper the iPhone's data throughput in a known good area.
Been a while since I've been to Apple. I can still go to the apple store and get a replacement if I bought it from t-mobile?
Yes you can.