Are there multiple endings to Dark Souls

You can kill NPCs in Dark Souls, just as you did in Demon's Souls. Some people kill Lautrec early on, for example, to obtain his very useful ring. If you ever accidentally harm a NPC, they will be hostile towards you, but you can "absolve" your sins at the NPC "Oswald of Carim" in the Church after the Bell Gargoyle fight to make them unhostile. The cost is Soul Level x 2000. Some covenants will also become hostile if you dishonorably leave them (abandon covenant without use of Oswald, betray their rules, etc.), which is also something that can be absolved at this NPC.

Unless you kill Oswald, you can always resort to this method to make the NPC's like you again (note that this won't revive them however if you killed them).

You might miss out on some story/sub-plots, but you should still be able to complete the game having killed all the NPC's that you are allowed to kill. It is hard to say for certain what the impact on the game will be as there are so many NPC's in the game with different functions.

Yes there are places that you can only get to by jumping. On the bright side however, they're not essential for progressing. Rather, they usually lead to some basic item or pick up. Off the top of my head, I've only discovered a light crossbow, bolts and one humanity in locations like this. Additionally, in most of these situations you can get past by rolling instead of jumping. From what I can remember, the bridge you're referring to is the most difficult jump I had to make.

The only other situation this is important, is done in order to return to the Undead Asylum (optional). You'll need to jump across to a ledge, but it can be done by simply rolling forward. Here is a video in case you're interested: