Well, for 1, consider spherical geometry. In Euclidean geometry, there can be only one line between any two points. But consider the lines on a sphere between the antipodes (like lines of longitude on Earth) -- there are infinite lines of longitude that connect the North and South Poles, not just one.
That's postulate 5, parallel lines meeting. Postulate 1 says that a line can be drawn between any two points. Drawing more than one line between a certain pair of points doesn't contradict that. If you can draw two lines, you can draw one line.
No. Postulate 1 says that for any two points A and B, there is a line AB connecting them. While you could argue that "infinite lines" are a superset of "a line" it is pretty obvious that Euclid meant one and only one line (which is true in Euclidean geometry)
You might observe that the way Euclid uses postulate 1 is to provide geometric constructions of shapes. If you want to argue about what he meant, what he meant was "you have a straightedge". Similarly, postulate 3 says "you have a compass", and postulate 2 says... "you have a straightedge".
You've described drawing several parallel lines that meet at two opposite points of a sphere. Postulate 1 has no problem with that - all of those lines are straight. Postulate 5 has a problem with it, because they meet.
