Having a longer rod is better because it makes casting a heck of a lot easier, and because the rod is longer, there is more...for lack of a better word 'pressure' on the fish when fighting it. If the rod is taller, the bend in it will be a lot bigger, tiring the fish out more. Not only that but it will be a lot easier on the angler... [imagine trying to land a spring with an ice fishing rod...not happening] When you are keeping the rod high and you have a big spring or steelhead on, it is definitely strenuous. Well this same strain is also put on the fish, tiring it out more.
In terms of what to do when a fish on... well yes you are right, letting the rod do the work is important. As the fish tires out, you will be able to bring it in easier [obviously]...so you use the rod to steer the fish towards you by giving it a bit of pull back, and retrieve as you bring the rod back down again. It's kind of hard to explain without pictures but I think I make sense
No, losing that monster was not your fault. Fish panic, especially when they feel themselves touch the bottom as they get dragged in close and it taking off towards the obstruction is only instinct. I can't even count how many times this has happened to me! It's just part of the challenge i guess.
Not sure what you mean by the side pressure, but I'm sure you did all that you could have. When fishing in tight spots I "worry about one thing at a time"...which often time means hooking into a fish while standing on something ridiculous, or right above a set of rapids etc...
All you can do when you feel the fish going into rapids is just ease off the tension on the reel [if it's a center pin then gently palm it] and let it fall back, as it may think it has escaped and swim back into the run, or if there is clear space you can just fall back with it, chasing it into the end of the run