I wouldn't go blaming the horses that you ride for having a problem with being on the forehand... I bet if an experienced rider hopped on the horse would come straight off the forehand. It's not your fault, you don't know what to do, but I'd be worried that this has gone on for so long in front of an instructor I'm assuming?
Your first question has been clearly answered so I won't go into that. The second question re: how does being on the forehand affect the horse and rider.
Number 1 It's **** uncomfortable!!! The horse has a hollow back, is stiff and will just fall into transitions, drop it's shoulder into corners which puts the rider off balance etc. making for a horribly uncomfortable ride. Compare this to a horse that is off the forehand, it is balanced, stays upright through turns, will jump into transitions with running on etc. The next step up from being off the forehand is to have the horse's back loose and swinging, where they really carry the rider and often it will feel as though the wither has just grown a few cm's in front of you- best feeling!
Being on the forehand all the time will make it next to impossible to get a nice topline on the horse, and often they have uneven muscles. This is why you're horse is stiff, doing exercises on the ground (stretches) will not do a huge amount to tell you the truth. Getting him up off the forehand, balanced and straight will be what does it.
There is absolutely no point in stretching under saddle and asking the horse to stretch it's neck out when it is on the forehand, as all it will do is lean on it's neck and front legs even more. Being so heavy on the forehand means it is 10x harder to turn as well. In order to ride a balanced turn or circle the hind leg MUST come under the horse's body to take the weight through the curve. If the horse is on the forehand it will compensate by dropping it's inside shoulder and swinging it's hindquarters out.
He may have some medical reason behind being stiff, but riding him on the forehand is going to do him more harm than good and you'd be better off to leave him out of work.
Joint supplements, depends on what is wrong with him. But like Spyder said, unless he has severe arthritis in his hind joints or a shockingly bad back, there's no reason why he should be working like that. Join supplements are not going to make him work correctly and muscle building supplements are not going to give him a topline.
To get him off the forehand, we are NOT your only hope, not by a long shot. You can't really explain over the internet how to ride a horse off the forehand other than a few generalised comments as everyone rides differently and every horse travels differently.
You can try lots of transitions (trot-canter-trot is the BEST for getting their back working!!), teach im leg yield so that he moves off your leg and understands to pick that inside hind leg up and under himself, LOTS of changes of rein etc.
My advice, quite going to these 'clinics' or goign to the instructor you're with now because they're not doing a thing for you. Hunt around and try out some different instructors in your area that will pick up your faults and get you working that horse off the forehand and correctly. A good instructor is your last hope, NOT a horse forum!