I think the advice you've gotten on training for a century is spot on. Increase your mileage gradually each week and try to do a couple of rides in the 70 to 80 mile range before the event. Two thousand feet of climbing over 100 miles isn't much, so it sounds relatively flat. If you like climbing, then by all means, climb. It carries a lot of training bang for the buck. That said, you also need to increase your time in the saddle, so do some long, flat rides, too.

Getting faster is, in my mind, a harder goal. I think you will see a modest increase in speed as you get fitter and as your body adapts to the stress of riding. That said, the only way to get markedly faster is, well, to ride faster. Find a group, if you can, that is a bit faster than your current comfort zone and try to stay with them as long as possible. Keep these rides relatively short--20 to 25 miles--perhaps. Interval training will also help, although I'm not expert on putting an interval plan together.

I was in your shoes more or less last year when I started riding. I made endurance, i.e., doing longer and longer rides comfortably, my first priority. From an aerobic standpoint, building a good base first lays the groundwork for speed work and hard climbing. I think you'd be wise to start there, too. Getting faster is a good goal, but I would suggest focusing on that only after you've build up your endurance.

More than anything, have fun and listen to your body.