You should definitely use the Pip System with values +1 to +4, but I think giving a name to each training level brings a more memorable idea to the player, for example "my character is a Master (+3) in stealth, but this is just a suggestion.
Regarding the sharpshooter issue, I believe it is the right way to go, accept an FP cost or condition it on another action, even better both if consider the attribute in duration.
To talk about the extra attack, I think it's important to talk about the levels, since you don't limit a maximum level in the system, there's no need for a level table, just let the game go as far as players feel good about playing, this can open doors for epic PCs or something like that. Think about epic feats os a bonus for the skills that goes beyond the "common mastery"
The way I would do the extra attack in the System presented as it is at the moment would be to put an athletics requirement ••, and reduce the cost to 1 FP, being able to perform only one extra attack per turn. As it is a "simple" feat (powerful sure), but you have to think that the PCs won't have a lot os FP to throw around between the rests, so a low cost with a higher requirement is in my mind the way to go (and spells can affect a large area and multiple opponents with a similar cost, attacks are single target)
As for the spells, I must assume that it's mostly my fault that it took me longer than necessary to get the idea, but in my view the idea of FP being in all the conditioning parts of the spells ends up hindering understanding. The way I would do it would be to place a base version of the spell with simple effects with a lower cost (1 or 2 for the basic version) and place a session afterwards with the higher FP cost effects. I believe that D&D 5e gets the training right in this sense.
Finally As for saves, I believe you've already taken the most important step and avoiding the 6 saves that D&D 5e uses, the biggest problem I see with a unique resistance would be, for example, mental attacks "attacking" a constitution-based defense. To keep it lean and at the same time give it a certain depth, I believe that the 3 saves are the right way.
I've been working on my own project but there is enough similarities that I would like to work with you and your system, if you ever need a little more brain power (great minds think alike eh?). If the ideia sounds cool mail me at bioignun3@hotmail.com
I really thought that it would take ages for a answer, it's great to know you are active in the work! :D