Seedling is becoming a bit pale and yellowing in some spots.

There are no species in the whole world that do well "pretty much everywhere"

The best way to know what works well in Florida is to go out and look in nature and in gardens. The species that do well in florida nature also do well in pots in florida. In garden centers the situation is a little bit different. Not all plants sold at garden centers is locally hardy. Check your USDA zone and compare to the plants hardiness zone. That is a good indicator.

Trees can be classified in different ways. One of them is conifers vs broadleafs. I am sure you can classify your seeds yourself with that information.

All trees have a yearly life cycle. Which means that they drop their seeds at the same time every year. The seeds lay on the ground until the conditions is right for sprouting. In temperate conditions it almost always in spring. In tropical conditions it is most common conected to the switch from dry to wet season. There are some places in the world where summer is arid and winter is wet. So some trees do not follow the rules given. Read up on species before sowing.

The best way to sow tree seeds is to pick them yourself under trees in your area when they fall. Directly sow in pots and wait until they sprout naturally.

The best way to start in the bonsai hobby is to buy mature garden center materials. It saves you 10 years of just growing trees and you can start developing bonsai within one or two years. Read up on features for good bonsai materials. While most species is apropriate for bonsai, very few specimens is. So shose carefully.

Azalea and cherry trees is not for Florida.

you can get the "eastern asian aestetics" without using east asian species. Actually localy hardy species makes it easier than struggling with non hardy species.

Here a good start for reading:

www.bonsaiempire.com/blog/bonsai-climates

But no self studies is better than joining a club and pay atention to what the local experienced bonsai artists is doing.

is there any online markets you know of to buy some seeds? 

As said before. Seeds is not the best way to start in bonsai. The best seeds are the ones you colect locally.

If you still want to grow from seeds and is absolutely sure that you have an urge to pay money for less quality, there are hundreds of seed selling sites. Just Google for tree seeds for sale.