Given your colloqulia I would believe that you are British.
Given your questions, I strongly assume that you don't have glacier experience. In the summer (ie: August) the only real difficulty you will have is glacier travel and altitude.
Given you don't know how to attach the rope to your harness (there are several methods used nowadays, including a pre-rigged autobelay device such as a grigri or a cinch to act as a pre-rigged jumar), and you have questions about how much rope should you have between your partners, I'd recommend that you get some instructions. Most years the crevasses should be pretty open by August, people still fall into them year in and year out. Crevasse falls should be considered serious.
Your headlamp is more then adequate, a plastic water bottle is fine if you wrap your jacket around it, to keep it warm. The rest of your questions should be answered when you learn glacier travel.
Check with the British Mountaineering Association about courses.