The best way to increase speed is hill work, as you climb up you have too work harder which is the equivilant to running faster on the flat. Try and incorporate a route that has at least a medium hill in it also try shortening you walking distance slowly and gradually increase the running.
With regard to breathing, i breath through my mouth while running and its isn't a problem for me. My advise would be to regulate it, i breath out on every second strike of my left foot and slowly breath in during the rest, it works for me.
With regard to speed, take it at your own pace, the only person you should be competing against is yourself.
I ran the brighton Half Marathon this year in 2 Hours 6 minutes, feb 2012, which i was delighted with. Unfortunatley 2 weeks later i broke my tibia plateau and collar bone in a freak running accident. I have a metal plate in my knee with 9 screws and also a plate and screws in my collar bone. Yesterday i ran the beddington park 10K in 62 mins, which although a lot slower than i used too run for me was a personal achievement.
Don't get caught up with what you think you should be able to do it in and just enjoy it. Running is supposed to be fun!!