Keep in mind your values are assuming the receiving antenna is on the ground.

LOS between two people (1.8m tall) is roughly 6 miles, almost 7miles  for Max VHF range.

For giggles I'll do my best to answer.  Original questions are in red.

-What's a watt of transmission power?
one volt-Ampere of power.

What's the difference between 5w and 8w?
3 Watts.  In practical transmission terms there isn't much difference except the 8W radio burns through it's battery faster.

Do antennas matter?
Probably THE most important part of your radio that you can control.  But to work optimally the antenna should be tuned to the individual radio (generally that isn't done with HTs, but as with everything there are exceptions).

-What are shortwave, cb, ham, frs, or gmrs bands? Who/how are they regulated?
In the US the FCC regulates them all and sets up the rules.  FRS and CB don't require any kind of license, GMRS requires a license (that can cover your entire family) and allows for more radio mods, HAM is a nickname for armature license radio operators.  Shortwave is a range of frequencies/band that cover HF to UHF.  It's an old term that was coined to separate the modern frequencies we use from the really long waves of early radio.

-What's a transmit frequency? What's a receiving frequency? Why are they different?
Transmit frequency is the radio frequency you broadcast on.  The receiving frequency is the one you are listening to.  Sometimes they are the same (like with FRS radios or when you use CB).  When they are different, it's so when you are broadcasting you can still receive (for example with repeaters).  When you don't use different transmit/receive frequencies that is called simplex communication.

-What's a tone? Why do we use tones?
A tone is a signal attached to the transmission.  It's used to turn off the squelch of the receiver.  That allows your radio stay quiet when you're not receiving a broadcast.  Otherwise you have to deal with static.

-What's a repeater? Why are repeaters so important? Where do I find their physical location?
That really 3 questions.  A repeater is a radio that receives a transmission and rebroadcasts it on a separate frequency (usually).  They can also have special features like tying into the phone network or connectable via the internet.  Repeaters are usually setup so the transmit/receive frequencies are a set distance apart on the same band.  However there are cross band repeaters that may receive on one band (2meters) but transmit on another band (70cm), this feature is included in some dual band radios.

They are important because they allow VHF/UHF radios to broadcast over much longer distances as they are much more powerful and will have a superior antenna that is much higher (see that earlier post).  So 2 guys with HTs can talk, under optimal conditions for 6 miles, with a terrestrial repeater I can contact people tens or even a hundred miles away if it's high enough.  Using a satellite repeater (and yes they exist) your HT's broadcast range is now roughly 1000 miles.

How can you find them?  There is a website, repeaterbook.com, with the locations of repeaters that clubs want to share, they also have an Android app you can use. But if you're a good HAM with a directional antenna, some driving and map skills will allow you to DF the site....

-How do I set my radio up so I can hear people I know, when they talk, from half a county away?
Set it up to the use the local repeaters.  For that I'd suggest using CHIRP, a programming cable, and the help of a local HAM

-Where do I find local emergency frequencies?
Talk with your local Ham, join the local Ham club (you don't have to go to all the meetings but it will give you access to more info), or contact your county EMS to see if they have setup public frequencies.  If you're LDS, see if your parish has a armature radio group.  I know the local LDS guys have a great network and they have generously incorporated our small Lutheran group.  Note the ARFCOM survival forum has their own emergency frequency list and you might go there to get the frequencies.

At this time I'll note in an emergency most repeaters I know of are taken over by the club that owns them and they set up a rigid net.  You must ask permission to join and have a valid license to enter the net.  Some clubs limit the net to their members.  We have a local club that has 4 repeaters during an emergency 1 UHF and 1 VHF are setup with these emergency nets, the other 2 are left open (however those are the two that don't have generators so if the power goes down...).  Again I will say this club was cool with us (Nerdy Lutherans) run a quick net during a snow emergency so we could check on our congregation (we have lots of elderly).   In my experience most hams are cool guys in an emergency and want to help, as long as you are licensed and follow the rules.

-I bought a BaoFeng radio. I charged it and stuck it in a drawer. What does it do?
Collects dust and provides false peace of mind.  If one doesn't know how to use it or what frequencies/tones to set it on then it's just a brick.

Knowing how to use is not just turn it on, set a frequency and push to talk.  If you want to take advantage of repeaters (esp. in an emergency) you need to know how to deal with a network.  In my area the clubs run a practice net on most repeaters weekly at a set time.  It allows everyone a chance to practice and/or test their gear.  Sessions are usually short, and discussions that may come up might include what IPAs are on tap at the local pub, or what antenna should you buy for your Chi-Com HT.

Yes that is much simpler

Buy a Kenwood V71A

Then watch this so you can set the radio up as a crossband repeater (which any of the dual band HTs could work through.

No.  But two of them could be setup as a crude dual band repeater.

The one I posted will do that, he shows how in it.

That's the radio I had mounted in my Jeep, till the 3rd rainstorm w/o a top killed it.  I need to replace or fix it.