A little wider than shoulder width is fine for regular pull ups.
Doing more pull ups is a game of patience, hard work and dedication. Failing the level is not a bad thing, the bad thing is not doing anything about it. I'd suggest you take it slowly, go back to level 4 and re-do it, as well as level 5, and then try level 6 again to see if you're closer. If not, keep going back to level 4, if you make level 6, great, that means you have good progress already. There's not a quick solution to doing more pull ups overnight, it's the same with anything, fat loss, muscle gain, or getting a degree at uni or any kind of success. Make sure you're patient, and don't get frustrated, the results will come if you're willing to put hard work both in nutrition & training and being patient.
About the dips, I didn't understand what you meant "wider", do you mean with your elbows flaring out? Don't do that, that could lead to injuries, focus on your elbows to your sides or as you call it straight back, always. I think flaring out has it's benefits, I think it hits the chest more right? But, to hit the chest more you have to lean forward, and boom, you're not putting your elbows at risk :)