Good questions and good response!
I have a few things to add and amplify upon.
First of all, BRAVO for having the right attitude about this and getting training. It's going to keep you safe while you learn. I'd like to recommend you pick up a copy of David Hough's Proficient Motorcycling for street smarts. It's kind of like the MSF training but a lot more comprehensive. Ken Condon (Riding in the Zone -- google it... good videos) is also big on street safety.
To answer your first, overall question: I'd practice low-speed stuff, street strategies and vision.
Low-speed stuff: When you're a complete beginner, things like turning from a stop, going down a sloped driveway into the street, coping with uneven or loose surfaces at a stop, etc. can be really nerve-wracking. Not to mention low-speed parking lot maneuvers (remember the infamous Figure 8?). Nerves can tense you up, so practice until you're totally comfortable wrangling the bike... stopping, starting, slow turns, etc. The fact that you passed MSF is great, but that doesn't mean you've mastered those skills. Keep practicing. Pro tip: You will go where you look. Look down, go down. Lift your vision and look where you want the bike to go. This is especially true at low speeds.
Street strategies: The good news is that this is a mind game, not something you need to do on your bike. Every time you drive your car (or ride in one), pay close attention and think about riding your bike. Look ahead. Anticipate. All that stuff. Get your head into your riding mindset. Think about what you'd do on a bike in any situation. Turn off your stereo and stop driving on autopilot... make your drive time learning and practice time.
Vision: Always, ALWAYS look where you want the bike to go. Target fixation causes a lot of crashes. Spot the hazard, but LOOK BEYOND at your escape. There are many, many crash videos where you can see the rider target fixate and freeze, riding right into what they wanted to avoid.
To answer your specific questions, Mr. Atom did a good job answering. Here's a bit of additional stuff to chew on.
1) Atom is right: Once the turn has started, don't make additional control inputs (the caveat is right too... you're a beginner, so we're keeping it simple). That means you should have slowed and downshifted (if called for) BEFORE the turn, so you'll be in the gear that you want coming out of the corner. Once in the corner, repeat this mantra: "One the throttle is cracked open, roll on smoothly and continuously throughout the remainder of the turn." Repeat that 10,000 times. Smooth. (PS: It's gyroscopic force
)
2) Agree with Atom. The Ninjette doesn't make a lot of torque so keep those RPMs up. As you gain experience and confidence, you'll find that the party really starts at about 9,000 rpm. It's a fallacy to try to link speed and rpm. What matters is whether you're in the right gear for any given situation. Stop focusing on the speedo... focus on the tach. Race cars and bikes don't have speedos! Geezer tip: If you can't wrap your head around ignoring the speedo, use "the rule of elevenses" Shift first to second at 11 mph, second to third at 22, third to fourth at 33, etc. Believe it or not, it works.
3) Starting a bike on a hill is a lot easier than it is in a car, because you can operate the brake and the clutch at the same time. The process is no different from the basic friction-zone work you did during MSF. Find a gentle slope on a side street or parking lot and practice. The difference between hill starts and getting going on the flat is that on a hill, you have to simultaneously work the brake, throttle and clutch. You don't need a death grip on the brake... a couple of fingers will do, and that will relax your right hand enough to operate the throttle.
4) Think of engine braking as, well, a brake. Your definition is correct. All it means is that you're off-throttle, so the wheel is turning the engine and not the other way around. It's what happens when you downshift, as the engine spools up to accommodate the gear you're in. As Atom said, don't worry too much about it. Focus instead on being in the right gear for every situation. Pro tip: You don't have a gear indicator. Get used to counting gears so you know where you are and don't get surprised by being in a too-high or too-low gear.
5) Ah, the great unknown. Yeah, it's hard to know how big the traction pie is. The bike has more traction than you think it does, and has a whole lot more ground clearance than you think it does. Given the way you're approaching this you're unlikely to get in trouble; you'll be nowhere near the limits of traction. The real point about traction is to be gentle. Don't grab brakes all at once. Don't whack the throttle all the way open while leaned over. Etc. Manage the resource... See throttle mantra (Throttle Rule #1) above. There's a lot to learn here about braking technique, throttle technique, body position, etc. For now, just keep it smooth but don't be overly timid.
6) It's a matter of getting used to it. Don't blame the equipment. It's just that you don't have experience. Back to basics... keep practicing and it'll come.
Have fun out there! ATGATT.