I've found that acceleration is a matter of technique over strength. The most effective way is the toe run, I find, unless you are starting from a dead stop in which case the cross over step is probably more effective. This is something you should look up, learn and practice till you get it.
Stand with a dumbell in each hand, holding them at your sides. Bend at your knees like you're doing a squat. Jump up as high as you can and land on the balls of your feet. Keep the weights at your sides. That's one rep. I like to do a few sets of 8 reps with 15 or 20 lb weights, depending on how I feel.
Are there any exercises and suggestions that would increase my agility?
Sprints is very good advice, but if there bad weather and you don't have room to do it and even if you would do sprints I would give you something extra. Buy jumpinrope and jump that rope with your toes. Did that as junior and it helped both acceleration and stamina/general speed. It's easy and you can do it easily every day in a week(or at least 6 times). So start being boxer
All the improving your strength ideas above are fine and improving leg strength will help some but without the proper technique you won't see much change. The thing I see the most with hockey players is that they skate with their feet shoulder width apart. That's great to keep from getting knocked on your butt and is fine once you're up to speed but from your initial start my suggestion would be to make sure that after each stride you bring your feet back together before the next stride. My feet actually scrape each other occasionally. This will almost double the length of your stride and will be applying power to your forward motion for a longer period of time. Make sure that you still have knee bend and good "snap" of the toe at the end of the stride. Try it real slow for a few minutes just so you can see what is happening and almost exagerate the motion. It might feel kind of weird or a little like figure skating and it is a little. Figure skaters skate with a tremendous amount of power and agility at the same time. If there are any national type figure skaters at your local rink? If so, take a few minutes just to watch them skate when the first start out and are just skating and stretching and not jumping.