Take your bike to a bike shop and get them to give it a good service, then help with a bike fit, even if only basic. If your old bike is broken in some way, and honourable shop will tell you.
Knee over the pedal spindle is a theory that was discredited back when your bike was new. It's still used by some fitters, even professional ones, but it means nothing.
To get your saddle height right, sit on the bike and put your HEEL on the pedal - if your knee just straightens, you're pretty close to right. It doesn't hurt if your saddle is a little low, just not too much.
The stem test doesn't really mean anything either. Base it on how comfortable you feel, the trouble being that you need some miles under your wheels to get your body used to cycling. You adjust reach by changing the neck (that holds the bars), not by shifting the saddle backwards and forwards.
You move the saddle to give you balanced position on the bike. For the moment, just put it in the centre of the seat rails.
You change the height of the bars either by moving the neck up and down the bars or buying a new neck. You can buy adjustable necks which can be useful. If you're lucky enough to have a bike with a quill stem, you can loosen the bolt at the top and slide the whole thing up and down - the bike shop will help here.
Constantly changing your grip is not a bad thing, it just means that you're varying the pressure on your hands and changing the angle of your back. It's all good and is why so many of us prefer drop bars because even on the top of the bars, you have a lot of hand positions to choose from.
Basically though, get your bike sorted out by a mechanic, get him to give you a basic bike fit, then ride the wheels off it. Eventually you'll know whether you want/need a new bike, but I'd give it six to twelve months. Equally, some never replace the old bike.