Hope I don't get a double post - my connection dropped in the middle of typing.
I think your confusion on the 555 stems from your schematic. The circuit you are using is not a good 555 circuit - it is OK for attaching a 4017 to a 555 that is already built and running. I suggest you do a search from your web browser "555 circuit" for tons of good info.
Here's one:
**broken link removed**
If you move down the page to astable operations you will see a good schematic for a 555. Also there is a little pulse calculator for you to use. You will see that if you use the values I suggested (R1 = 1k, R2=68k, C=10 mfd) you will end up with a 1 Hz pulse in a 50% duty cycle. The sample schematic should answer your questions. As you proceed, add a LED and dropping resistor between pin 3 and ground so you can watch the action.
To answer your first question about the necessity for R2, go to the calculator on the web page and simply raise the value towards infinity (no resistor) and see what happens. Remember I said earlier that this was "the most important element?" You might also put a 100k variable resistor in here so you can watch the pulse time change.
Question 2 - Please accept that yours is NOT a schematic for building a 555 in astable configuration - it is for a 4017. You can easily select a good 555 circuit from your search mentioned above.
Question 3 - There are many ways to get a 555 working and different people will recommend different arrangements. If you are looking for a stable, dependable circuit, stick the cap in there. Also, you can add a 47 mfd electrolytic from pin 8 to ground (put it close to the pin) for decoupling. I add these because they are easy to get and cheap. I do not add any superflous parts in my circuits - I believe in simplicity.