I am not that experienced with electronics, so this might be a silly question. But I dont know. Assume that I have connected some electronic circuit (transistors, leds, anything else) to the Arduino pins, is there any chance that I damage the hardware if I change the pinmode to input? What role do the integrated pullup/pulldown resistors play? Basically, is it possible to create some "unintended" flow of current, that damages the board or external hardware, if I change the pinmode or disable/enable the pullup/pulldown resistors (or something else that I dont know about)? Can I break the hardware by programming mistakes?
You are coming with some good questions about a complicated subject. You will be going through a learning process. If you do not violate the design parameters of the micro (voltage and current to name a few) you normally will not damage it. Knowing all of those parameters and what the circuirity surrounding the micro has a huge impact on your what can damage your micro and design. Without a schematic, this will change with each circuit and integration, it is impossible to give a definitive answer but I will take a SWAG.
Question: "is there any chance that I damage the hardware if I change the pinmode to input?" and it depends on what mode the pin is in before you change it and what is connected to the pin. Generally you will not damage it assuming your voltages are equal to or less then the voltage supplying the microprocessor and the pin is not connected to an inductive component. You can get changes in your external hardware.
You ask "Can I break the hardware by programming mistakes?". Again I cannot give a definitive answer unless the circuit and what is connected is known. LEDs etc are generally no problem. If in doubt place a resistor in series with the load, something in the range of 330 to 500 ohms and see what happens. If you turn on some external device that damages stuff that is one possibility.
You ask: "if I change the pinmode or disable/enable the pullup/pulldown resistors..."Probably not but it depends on what is connected to the pins. Generally if the pull up resistors are needed such as for a button turning them off will cause some intermittent problems where it is on then off but that will not damage the micro, the effect on external devices is unknown as are the devices.
This stuff is not going to be assimilated in a few days but over a much longer period. There is always more then one way to do a project, the best is probably what you decide. You will make mistooks, and possibly destroy some of your Arduinos, this is to be expected, that is why I have spares. The most important part of the process is to enjoy and have fun.