From what I have read on other posts, you can only proc one skill from each category (opener,attack, defense) on every attack. So if all your skill are from different categories then all 3 could proc on one attack. If you have two from same category then only one will proc, per attack. But if you are talking about throughout a whole battle, then yeah you will probably be able to use all of your skills (even if they are all attack ex.) if you stay alive long enough and are able to get in enough attacks. Which skill will proc is selected randomly before each attack.
I'm not sure, but I don't believe that adding two skills from the same cat will lower proc rate. I don't know why it would. But, it probably would not help either because you are still only getting one skill that procs (per category).