to answer your direct question, all drills/matches done post league draw (day 3) will contribute to SA skill growth
drills that train physical attributes in day 1 and 2 of the season will cause skill growth in those attributes even though SA skill growth is toggled.

ideally, you would be putting FK SA on a player that has already proven themselves good at taking them.
the best fk takers in this game are (usually)those that have the crossing, passing and shooting stats high
i recommend drill regimens that develop all 3 of those abilities
there are exceptions but generally the best fks takers are AML/AMRs
i have a MC whos shooting stat is abnormally high (165%) who i put a playmaker sa on and he takes dead balls for me on one side, his crossing is trash at 72% but he contributes goals and assists so you can't always pay attention to numbers
on the other is an AML/AMR with 140% attacking stats

i would recommend identifying which players, ideally no more than 4, that you want to take fks for you and then doing testing and observation to see who performs best from which side. It takes awhile and some tinkering but results are worth it.

My only player with FK SA is an academy grad that rarely gets appearances. I don't rank it as highly in importance as I used to.