I learned that it helps to avoid a reset whenever Serial Monitor connects, to have a nice capacitor (10 .. 47 µF) between RESET and GND.
I guess USB would normally pull down the RESET pin to GND via a resistor, at least in the way Serial Monitor opens that connection,
but that signal is too short to discharge the cap far enough.
Now I was wondering if one can use a digital signal to Enable/Disable this feature. Can Arduino signal a "Don't Disturb" or "Ready to be Reset / Uploaded" ? How can such a signal be wired to the RESET pin?
Connecting PIN13 being high to RESET would probably inhibit a reset, but I fear even the reset button would not work any more, and on the other side, if PIN13 is low and connected to RESET, the arduino might not start at all ?
I'm not too familar with dealing with electronic signals and ran into the terms mentioned in the Subject, feeling they are related to my issue.
Can anyone explain how, or why it can't work ( the latter in a way I understand, if possible 
If it goes beyond a few resistors, diodes and that magic capacitor, feel free to add Inverters and other Logic bricks...
Can there more be done with that "EN RESET" trace than cut/resolder?
Can I break something by eperimenting, short cutting etc., as long as I stay within that 5 Volts universe, power comes from the USB cable,
and I always use a resistor with my leds ?
I'm new to the Arduino, and i don't understand what the pin-13 connection (through a capacitor) is doing... The reset circuit is already ORed (actually NORed) with the reset button.
Connecting pin-13 being high to RESET would probably inhibit a reset...
Yeah, and if you make a hard connection to +5V (no resistor) pressing the reset button will short 5V to ground.
Removing the capacitor (C5) will break all connection between pin-13 and reset. Someone else will have to jump-in and explain the effects/consequences.
Can I break something by eperimenting, short cutting etc.
Shorting is generally dangerous. (Dangerous to the parts... not dangerous to you... ) You can get excess current and burn-out parts. Often, you can get-away with things you should never do, like accidently shorting an output to power or ground, but you can blow the chip so you shouldn't try it. (Shorting the reset to ground won't "damage" anything... You'll just get a permanent reset condition. 
) Cutting traces and opening circuits is generally safe. "Randomly" connecting-up capacitors or higher value resistors shouldn't damage anything. I'd say a 10K resistor connected anywhere on the board very-unlikely to damage anything. I'd be "careful" with values less than 1K.
I'm new to the Arduino, and i don't understand what the pin-13 connection (through a capacitor) is doing
Me too, I'm new to microcontrollers in general as well and have only rough understanding of the electronics. (can calculate Ohm's law, roughly understand the behavior of a transistor (even BJT vs FET) ).
I just learned that Arduino pin13 is easiest to use as output, as it is already equipped with a led.
if you make a hard connection to +5V (no resistor)
My guessed rule: one should never directly connect any output pin to GND or 5V as this will produce a shortcut, if the signal is in the wrong state.
correct ?
Dangerous to the parts... not dangerous to you
yes, that's what I fear more. I'm sure to survive my Arduino, but that should not be proven true too early
The reset circuit is already ORed (actually NORed) with the reset button.
Does that mean that pressing the reset button connects the RESET pin to GND directly ?
I guess this question leads us back to the subject : how to combine multiple signals to one : Pull Up / Pull Down / Wired OR ???
And how to add an additional signal to the pre-wired reset logic?
My guessed rule: one should never directly connect any output pin to GND or 5V as this will produce a shortcut, if the signal is in the wrong state.
correct ?
Yes, the magic number is 40mA never take out more or allow it to take in more otherwise damage will be done.
Does that mean that pressing the reset button connects the RESET pin to GND directly ?
Yes, this is fine because that pin is an input and they have a very high impedance so you can connect them to +5V or ground without issue.
I just learned that Arduino pin13 is easiest to use as output, as it is already equipped with a led.
Not sure why it makes it any easier but the indication is nice.
However your idea won't work because the reset button connects directly to ground and if PIN 13 were to be set high and someone were to push the reset it would shirt it out.