What does 0/0 = and other 0 questions

Question 1 0/0

Is it 1 or infinity or simply undefined?

I realize that 4x0=0 implying 0/0=4

AND 5x0=0 implying 0/0=5

to infinity.

Whelk-graph1overx_medium

What does this graph even mean? I realize it's for convenience sake but once x=0 it just stops existing?

But my point being, if anything divided by itself is 1, why not zero? Am I missing something obvious? We already have that weird rule about things being raised to the zero power, why not just stick an asterisk in the math books and calculators and call it a day.

Question 2 If division by 0 is infinity then ∞/0 = 1 or 0... right?

Question 3 is 0^0? I have Googled this and I don't understand the forum answers.