Congrats on a successful first insertion! I also have a small Lunette, so I can attempt to answer all your questions.
1- I couldn't find any folds smaller than the triangle, so that's my go-to fold 95% of the time. When I'm in the shower, I can't get the triangle to open, so I use the punchdown with the punched part facing up.
2- I try to feel around the bottom for dents, but you're right that it's hard to really check if you can't reach the rim all the way around (and I can't either). I spin the cup with just one finger rotating the base of the cup, and that forces it open if it's not already there.
3- Actually, I use the same spinning trick to check for a seal, too. Not counting my very first insertion attempt and when I try to use the triangle fold in the shower, my small Lunette always opens and seals on the first try, so it probably is as easy as it seems.
4- I think the small Lunette has a high capacity compared to your flow (20mL in the cup and 6-15mL in the various tampons), so you shouldn't need to empty it away from home (and I've never needed to either). If you have to empty it at school, just wipe it off with toilet paper and reinsert. I think those feminine wipes may be trouble, as the chemicals could upset the vaginal pH and trigger an infection, so if you can't rinse with water, try not to use anything on it at all.

this was very helpful! thank you for responding (:

Ha! You like the punchdown fold facing up, I like it facing down.

Facing down, I use my index finger to create an air channel and my finger feels the cup open fully. Then I nudge the stem/base rearward and give the cup a boost as I Kegel it up and into place. No need to spin or swipe or anything because I know it's open and facing the right way.

I've never been able to spin any cup. That's "a" way to get it to open and seal, not the only way.

And yes, the small Lunette has a surprisingly high capacity -- higher than many "large" cups. Start by checking it as often as you'd change a super tampon and then adjust the timing from there.

I usually give my cup a quick rinse before re-inserting if I'm home but if I'm not, I just dump it and re-insert. Those few drops that remain don't make any difference. And I figure that the more I handle it (by wiping, etc) the more chance I have of =8oO dropping it.

1-- Origami fold is pretty small.

2-- Some women can reach all around the cup, some can spin the cup. But a women who’s kind of “tiny” might not be able to do either one. On YouTube, I’ve had very young teenagers tell me that they just sort of “wiggle” the cup (pinching at the base) forward, back, left, right.. Just in really small, gradual movements. And often that helps with a seal. Even I, as a married woman, find it a little uncomfortable to reach up the front side (sensitive urethra in the way, just at the opening). Another thing you can do is, since you say you can reach into the back part-- try inserting so that the folded part is facing the back wall. Because dents are usually on the side where the crease/fold was. That way, you’ll be able to check.

3-- Making sure its popped open is the best way to ensure a good seal. It usually won’t pop open all the way, unless its inserted properly. Also, giving a gentle tug downward sometimes helps. Once in a while, if we get into a rush, and don’t check it properly, we might get less than a perfect seal. But usually with practice, you get to know what does/does not make a good seal for you.

4-- The small Lunette has a pretty decent capacity. The first time you use it, just check it every couple fo hours, to see how full it is. You will get to know your flow. For public bathroom cleaning, most women just keep some bottled water in their hand bag to rinse in the stall with. You can also wet a paper towel (toilet paper tends to shred apart) before you go in the stall. With commercially retailed wipes… It really depends on the ingredients. Many of them are meant for use on the outer genitals only. As far as biological compatibility goes, all over the body, the outside can tolerate things that the inside cannot. The inside of the vagina has a delicate p.h. balance, so if the wipes have anything in them that could upset that, such as oils, lotions, cleansers, fragrance, light chemicals, etc., it could irritate things. I know some baby wipes certainly do have those things in them. Quite honestly, you would be safer off using a plain water-wetted paper towel, and you would also save money.

1. You may find that it is easier to insert your cup if you use a bit of lube. Saliva can work too, in a pinch. During the first couple cycles, I kept a bottle of (water-based!) lube in the bathroom for this very purpose, however, I am now proficient enough with my cup that I no longer need it. You can use the "folds" tag in the side bar to look for other folds, though.

2. Stick a finger inside once the cup has been inserted. Feel around the base a bit. So long as the cup doesn't have any dents, it has opened. If you are having troubles with your cup opening, run it under cold water just before inserting it. This is often necessary with my Lunette, as it is very soft.

3. Some girls tug at their cup to ensure a seal. Others spin it. I do neither. I have gotten to the point with my Lunette where I trust that it will seal up if I Kegel it in. It's never failed me. You can use the "seal and suction" tag for more ideas, though.

4.The capacity of your cup may vary a bit. The cervix often steals a bit of space in the cup, so it isn't always possible to go off of the tampon sizes that you used previously, anyways. It's essentially something that you will learn over time. I would highly recommend an account with MyMonthlyCycles.com. You can track you periods, make note of clotting, color, PMS symptoms, weight, and flow level. After a few cycles have been recorded, patterns will begin to emerge. You will know to expect a heavy day on the second day of your period, for example, where you will need to be a bit vigilant about emptying the cup, and you will know that on the last day you needn't worry about it at all. You'll get a pretty accurate idea of how long you will have between periods, as well.