Is a four-digit PIN safe?
Where wrong tries are limited, mostly yes: a card that locks after three tries gives a guesser 3 chances in 9,976. Where they are not, no PIN is safe, and a password belongs there instead.
Why are 1234 and 0000 never given?
They are the first PINs anyone tries, so a person handed one would rightly distrust it. Leaving out the 24 obvious four-digit PINs costs less than a hundredth of a bit.
Six digits or four?
Six where the device allows it: a guesser with ten tries has 1 chance in 99,998 instead of 1 in 998. Phones and many apps take six, and some take more.