Couple of things there, and for all the actual EEs out there apologies for butchering all sorts of physics to summerise this.
Current will be the same anywhere in a circuit. So it can't disappear. You need to look at ohms law and how it applies to things in series,
http://www.build-electronic-circuits.com/ohms-law/
https://www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.example.ohm.html
In the real world we don't have perfect wires or resistors so the real model of a output pin driving a lamp has R values for inside the chip (drive components), the wire, the lamp and the power supply *. So for a simple drive we could say 1ohm from drive components, 0.1 ohm in the wire 9 ohms in the lamp and 0.9 ohms in the power supply. Totals to 10 ohms which at 5V will have a 5/10 = 1/2 amp current flow (outside a chip drive pin but well within a good driven transistor). If we screw up the alligtor clips and short the lamp we get 1+0.1+0.9 ohms of resistance = 2 ohms. 5V/2 = 2.5 amps current flow. To put that in perspective we can use the power forumula
Power = current & voltage for an answer in watts. 2.5*5 = 12.5 watts. Which isn't enough to boil a cap of water instantly but will happily vaporise any transistor smaller than your thumb. If we had put a 2 ohm series resistor in there the effect on the lamp brightness would be measurable but low, but would halve the worst case current flow, which depending on design might make the difference between an oops and needing to replace everything.
So for point one the resistor doesn't 'absorb' the current. It acts as a choke that prevents the worst case flow from being impossibly large, water example would be constricting a hose so that even if the end falls off the hose will not thrash around dangerously
With surges in capacitors, yes when everything is in steady state capacitors do smooth current flow. If however we added heaps of capacitors to make our LED power supply stable that means if we have a massive startup current as they all need charging up. Which may happen unexpectedly when we flex that poorly soldered cable. Flow on result from that can also be that our power supply goes from zero to max drive capacity suddenly, droops downwards under the charging load then the capacitors reach full charge but the drive circuits in the power supply are slow to respond and over shoot and suddenly our 5V power supply is now driving up to 7 volts, which will push back into our 5V output pin with damaging results (all explanations above are conventional curren).
With the impedance matching there are several layers to it that you need to work towards, but for the moments suggest using the mental model that for optimal signal quality we want to keep voltage*current consistent along the cable, and therefore anywhere were we change cable design we may need to do some form of matching to avoid fun effects.
Impedance is a deep topic that at it's extremes in the high frequency RF starts to just not behave rationally. For the moment strongly recommend doing some worked examples on Ohms law, and then moving onto how diodes work and how to calculate when they are in circuit and conditions are constant (DC). Transistors are possibly further than you want to go at the moment but applying ohms law to make sure things don't go bang is something you do need. Just be aware that what happens when signals are changing(AC) is deeper and holds some unexpected surprises that you will find as you build more things and can either learn by experience or by reading. I've done both and the smoke from experience certainly stuck in my mind better.
http://www.evilmadscientist.com/2012/resistors-for-leds/
And further reading
http://www.evilmadscientist.com/?s=basics
* more complex in reality but power sources can be considered to have an internal resistance when determining effects of of load. A 9V single battery has a high internal resistance, so will not produce 9V into a big lamp, where 6 1.5V D cells would, because they due to physical design allowed by their size have a lower internal resistance. Ditto 12V of AAs won't start a car but 12V from a car battery with internal resistance in fractions of an Ohm will.