First is fine Second is incorrect, but only due to the fact that it would be "My friend and I". The third would be "are" and not "is", due to the fact that two is more than one and therefore is plural, and plurals need "are". The fourth is correct, however it's missing punctuation. "We can't drive on: all the tires are flat" or "we cant drive on, all the tires are flat." The colon (:) is used for adding information to explain the previous point in more depth, whereas a comma (,) is used for to create a pause in a sentence.

"I need nothing from him," is good. "I and my friend shot a film about wild animals in Africa." - "I and my friend" should be switched. "My friend and I shot a film about wild animals in Africa." "There is two kilometres left to Moscow." - You'd want to change 'is' to 'are' because you're talking about multiple kilometres. "There are two kilometres left to Moscow." "We can't drive on all of the tires are flat." - This will be fine if you just remove 'on' and put 'if' in its place. "We can't drive if all of the tires are flat."