"...I might have hit the front brake. But had forks turned completely to the right and it slowly went over...."
If Im reading this right you used the brake while the bike was turning and the bike went over.
Im afraid you have discovered from experience one of the things you will learn in the MSF course: never brake the bike while turning.
It does not matter if you are going 90mph or 1mph. Turns and corners are one of the things that are different on a motorcycle from driving a car. You must slow down when approaching a turn, corner or curve, set up your speed before the turn, countersteer into it at normal riding speeds, or turn the handlebars into the turn at "walking" speeds, and then continue thru the turn at a constant steady speed.
As you exit the turn you give the bike some gas to straighten the bike up. On a big sweeping curve at normal speeds getting on the gas and feeling the bike pull itself straight as you ease up on the pressure you are pushing on one grip to counter steer, is one of the things that makes the bike so amazing to ride.
Somewhere in the last 20 seconds you asked yourself "but... what if I have to STOP in the middle of the turn?" Then you must straighten the bike first, and then brake hard once the bike is straight. To straighten the bike at normal speeds push on the opposite grip to countersteer the bike in the other direction from where it was going, then brake to stop. If you were going thru the curve as fast as the bike can possibly go, you are going to be in trouble if you have to do this. That is why you look all the way thru curves, take the outside-inside-outside path, and do not ride at the edge of traction on your tires, unless you are on a race track, and this is your 200th lap around the same course, and you have been walking the bike up faster and faster on your practice laps and know exactly how fast you can take each curve. Not possible on the street.
One other thing: when you are taking curves at normal riding speed you keep your head in line with the center of the bike, you lean with the bike, not more, not less.
When you are making a U turn or going around a corner let the bike lean to steer like a bicycle, but keep your body and head vertical, and twist your head and shoulders into the turn to look where you are going, and to allow your shoulders to turn with the handlebars all the way to the limit of its turn (hitting the stops).
Sorry you dropped your bike. The motorcycles that are used at the MSF course do not have mirrors or turn signals, because they sometimes get dropped. Then the only thing that gets bruised is our ego.
Im afraid you have now qualified for a 'personal experience' of the merits of taking the MSF course to get your license. In the class an instructor would be watching you everytime you practice a maneuver, and will tell you if you are doing something not right, and how to correct it. I can still hear my instructor telling me over and over "keep your head up - look where you are going...." I was use to riding a dirt bike and kept looking right in front of my front wheel (for the rocks and ruts that were not there :^). Mirrors and turn signals and handlebars are surprisingly expensive to replace. If the course keeps you from dropping your bike even once, it has paid for itself.
One more thing: you dont normally need to turn your bike immediately from a stop while riding. At a red light for example you have a few car lengths to get the bike going before a turn from a stop. But if you do need to turn you bike from a stop, in a parking lot for example, while you have your feet down turn the handlebars all the way and lean the bike a bit in that direction while your feet are still on the ground, then start to engage the clutch into the friction zone and feel the bike pull ahead into the turn. This take practice, and they do not have you do this during the MC road test.
Also, once you have been riding for a while and have some practice, then you can start to learn how to slow down in a curve at speed, and even use the brakes. What will happen if you slow down in a curve at normal riding speeds is the bike will lean harder and harder and turn tighter and tighter into the curve, unless you correct for it. That is an advanced riding skill.
For now, whether going slow or fast: no brakes in a curve or turn. Use the friction zone of the clutch to control the speed at walking speeds and steer the bike out of the U turn if its going too fast - and get the bike straight before you use the brakes to stop.
And also: Put your feet down when you have to.