Ratings are random in their adjustments, but each player is assigned a hidden value to determine the general direction (if you're into statistics, they are all assigned a mean but have a pretty large standard deviation). You'll find some players boom, others will bust, and most will have a small general movement one way or the other with an occasional blip in the non-trending direction. The current values will always move towards the max, but the max may go up and down from the above description.
Your player's development is influenced by his coaching staff - mostly by the head coach, then by his coordinator, and then by his position coach. So if your coaching staff hierarchy is poor in an attribute, the players will take longer to develop that attribute. In the first year there's not much you can do about your coaching staff, but in early free agency you can hire away coaches from other teams as long as you are offering them a promotion. Oh, and coaches will trend just like players do, including a decline as they age.
For kick holding, you should be safe from injuries. Injuries are determined by actual collision events, which are very unlikely for the kick holder (the exception maybe being a botched snap). The kick holding attribute is what you want to look for here - that's pretty much the only influencing attribute, and has a small impact on the kicker's accuracy as well as the botched snap potential.