Maybe this will help you. Nice clear guide to soldering, showing component leads being bent to hold the part in place!
https://learn.sparkfun.com/tutorials/binary-blaster-assembly-guide
Looking at your photo, it looks mostly fine - you just need to trim those leads! You don't need to clean off rosin flux. Any other kinds, just make sure it's described as a "no clean" flux.
To be honest, from your description and photos it looks like the iron isn't hot enough and you are holding the iron to the joint for too long. Hot and quick is the way to go, and wipe your tip very often. You just need to practice, and learn to get the right amount of solder first time. Tin/Lead solder is easier to use, so as a beginner you should be using that. Lead free solder tends to be a bit gloopy. Don't worry about exact composition for now, you don't have the experience to appreciate the difference. Also, you are not doing enough soldering to have to worry about health risks.
Looking at the temperature ranges you have given, (and to put it into units I can understand!) 500F = 260C, too cool for soldering. 600F = 315C, ok for very small joints, 700F = 371C, ok for mid-sized joints. A lot depends on the size of the iron tip though, it has to be able to store a certain amount of heat to transfer into the joint - so if the iron tip is small compared to the joint, it needs to be hotter because the joint will cool it down more, and if it is large compared to the joint, you can have it a little cooler, but you may find problems because of the size. But a bog standard 30W mains iron with a standard tip will do 90% of through hole joints 90% of the time, and the other 10% just need a bit more care. As I said before, if it's too hot you can extend the tip out a bit so more heat is wasted. Looking at the board you have soldered, you need a mid-sized tip, very ordinary and boring. The sort that is round and cut off at an angle seems to be the easiest to use (called "bevel" or "hoof").
(Edit: KISS - I started writing this a couple of hours ago, before you posted the video - good video!)