To clarify, because it hasn't been given as an answer yet, the 'gunslinger' itself, the weapon that you use that allows you to build Mini-Sentries, does not have an HP-regen ability. It grants you additional HP, guarantees a crit on a third consecutive hit, and does not random crit, but the item itself has no further special properties.
Formerly, the Mini-Sentries that a Gunslinger could build would always deploy at full health. This had the unintended side-effect that was likely what the SPUD user was referring to - a mini-sentry in the process of being built would constantly regenerate its health until it finished building, making it nearly impossible to destroy before it finished deploying (unlike normal sentries, which can very easily be destroyed before they finish their initial building animation).
This has since been patched out, so that mini-sentries no longer infinitely regenerate health while being built.
That is an interesting question, and I found an answer to it.
http://loadout.tf/
This website allows you to customize loadouts on a model of any of the 9 mercenaries. While it does take a while to load some times, it allows you to select weapons, cosmetics, and poses for the loadout, so you can see how your items of choice look with eachother. It will even warn you when two items clip and can not work with eachother.
To select a class, click on one of the portraits at the top of the screen, and select add item. This will bring up a menu with all items the class you chose can equip. Select the items you want to add, and they will appear on the mercenary in the background. Click outside of the add items box to close it.
To select a paint, first the item must be paintable (duh). Once you add the item to your loadout, select the paint bucket item in the upper left hand corner of the box that has the item you selected. At the bottom of the paint list that appears will be the Halloween spells, and will even show them changing colors, much like in the game.
If you already added and item, and want to add paint to it, go back to that items box, click on its paint bucket icon, and select the paint you want.
Best Answer
When you sign up on the main menu, you will get an alert when someone has asked for a coach.(Usually very quickly)
If you accept, you will be automatically connected to the server they are on in a spectators type view. The chat and voice chat are both limited to the player you are coaching. Also, you have a few extra features, such as "Go Here","Attack This", or "Defend This" that you can place anywhere. There is a limit of 30 units you can travel from the student.
What's usually expected of a coach is general friendliness and patience. There's players are generally new to the game and want to learn. However, you will come upon trolls who just want to waste your time. There is no punishment for leaving a student early.
After your time with eh student is over, you will be put back into the main menu.
You can then "sign up" again and get another student to teach about the basics of the game.
My tip for coaching is to point then towards the easier classes to play, then advise them to try out different classes once they get used to the feel of the class. Make sure to tell them not to worry about deaths, it's part of the game.
Overall, just give tips, be nice, and lead the way in not being frustrated with this awesome game.