> What is a burner?
It's just another piece of (cheap, starting at about 20$ or so) hardware that can program a blank chip that comes straight from the factory. It can also be used to set/unset some configuration bits (called fuse bits). www.adafruit.com
has cheap ones that work (e.g. USBtinyISP).
> What is a boot loader?
It is a small piece of software pre-programmed to the micro controller that can talk to the PC using serial. It automatically starts after a reset. It's meant to ease to process of getting code onto the chip (avoiding to use a 'programmer' / 'burner' ...).
Sometimes this piece of code can get trashed and you need a programmer to restore it. It's also possible to write code (e.g. with the watchdog timer), that leaves the chip in a state so the bootloader can't work.
> The Bootloader
Will be on the chip, if you buy an Arduino board. Chips bought at normal suppliers are blank.
> The Burner / The IC programmer
> The AVR
AVR is a brand name by Atmel Co. that classifies a certain type of chip family they sell.
> The IDE
The Arduino Software. Integrated Development Environment.
> 1) Develop my own Arduino application project, to produce a stand alone RBBB to perform according to my own sketch. Produce a stand > alone Board, which I will program with my sketch, using a USB port and cable.
No problem. I do that too.
> 2) Re-program an existing stand-alone Arduino kit, to change some inputs, units, parameters, to allow it to work on my car.
> For this second task, Is it possible to download the existing sketch to my PC, print it, re-program it, and upload it back to the board?
> What would I need to do so?
You can only download machine code from the chip. You can also disassemble it, but that will not give you the easy human readable c/c++ code. Only for experts/geeks/nerds.
> Is it possible that I unplug the AT328 IC from my board, extract the IC from the stand alone board, plug it into my board where I have
> my sketch, re-program it, and plug it back on the stand alone board? Will the two IC´s be destroyed or such?
As long as the bootloader is on the chips you use, you can do that, no problem.
Given that programmers that work with AVR chips are quite cheap it doesn't hurt having one of them too. That way you can skip swapping chips around and program the chip in it's circuit. (ICSP programmer: In Circuit Serial Programmer). The day will come when you will need a programmer. It also gives you the option of just buying 'normal' AVR chips at your favorite supplier and save some money (a few bucks per chip).
Hope that answered some of the most pressing questions.