Cultivars are selections but do not necessarily breed true to type. If you grow seedlings from them the seedlings will be variable and not necessarily true to the parent. The genes can be variable. So in your example/question #1. The seedlings will not be 'osakasuki'. It is hard to say what you will get but say you got 100 seeds on your plant from that cross and grew them out....you would probably get all types. Maybe some red, some green, they would vary in leaf shape and growth rate etc. Lets say you grew all 100 seedlings to maturity but there was one in that 100 that really caught your eye. It had a good growth rate, nice shape, disease resistance, great color.......lets say it was exceptional and really stood out from the crowd. Perhaps that one would be worth giving a cultivar name. Perhaps you register is as Acer palmatum 'Heruga'. To keep those characteristics true, so other people could grow it, it would need to be propagated from cuttings/graftings. Some of the others in that same seedling group may be mediocre or even ugly and/or poor growers.

2. Well that gets tricky. Most likely not. Species are species for a reason and don't go randomly mix. There may be a genetic incompatibility, or there may be a difference in flowering time, or flower structure or etc. etc. Obviously some closely related plants (Or animals) can cross, sometimes made easier with man's help, but species don't generally cross easily, and it is hard to predict what will and what won't except by trial and error. So it would be more likely to be able to cross a A. palmatum with perhaps a closely related maple, less likely (and probably not at all)with an A. rubrum, even less likely (impossible) with an oak tree or a rosebush or...... Got I?. Some (not all) closely related species can cross. Similar in the animal world. You can cross a donkey and a horse (or even a tiger and a lion). Such crosses would not happen in the wild (and in these animal examples the offspring are sterile.......which can (or not) happen with plant hybrids too). Some do cross. Oaks are notorious for crossing with closely related species and if you are identifying oaks in the wild you will often find trees with intermediate characteristics between two CLOSELY related species. However, ifspecies mixed too easily......there would be no species.....everything would be a blend of everything else.

3. Similar to #1. Your 'Thunderhead' is a CULTIVAR, so your seedlings could be variable and different.

4. I don't know how easily they cross but if she is a reputable nursery she is probably selling pure seedlings. If you raise seeds of pure species under normal conditions you normally will get pure seedlings (of the species). Note if you raise things like citrus or apples from seed you will get a LOT more variability in the seedlings as these manmade plants have fairly complex and variable parentage. The offspring will still be an apple or a citrus but perhaps otherwise very different than the parent plant.

Thanks for the informative reply. Gotcha on the Japanese maples. For the pine, I also have pure pinus thunbergii species plants. Is it possible that they can pollinate with other pure pines like pinus strobus, Parviflora, densiflora etc? I want to start propagating my pinus thunbergii seeds once they start producing. Can I expect the seeds to become true pinus thunbergii species when there are other pines around?

I would think they would all be Pinus thungergii