Basically until you get comfortable with the combos, you’ll want to stick with slightly easier links, as dropping a combo altogether will always yield less damage than not dropping a slightly easier one.
The “l” is for “light”, so when you see something like l.tatsu or h.shou the letter before the period means to use the light, medium, heavy, or EX version(similarly, in case you were unsure, on normal moves cl. = close standing, cr. = crouching, s. = far standing, j. = jumping, and nj. = neutral jumping).
As far as FADCing, the two main benefits are that you can extend combos at points where you otherwise couldn’t, or you can safely back out of an otherwise unsafe move. An example of the first is that you’ll notice that tatsu loops generally start with cl.hp or cl.mk. However, both of these moves require you to be directly in the opponent’s face, which they’re obviously not going to allow you to just walk up to most times.
One of your main tools will be canceling cr.mk, which is fast and has great reach, into h.shouuken. You can FADC the third hit of h.shou, and the hitstun from it will leave just enough time to land a cl.hp, and perform a tatsu loop combo from there, essentially allowing you to get the great damage and stun of a tatsu loop but from a much further distance out. Disclaimer: this is one of her harder combos and will take you a good while to get down, don’t get too far ahead if yourself.
Similarly, you can FADC out of the fifth hit of ex.shou and continue a combo, which in effect allows you to pass through most attacks with an invincible startup combo-starter whenever you have at least 3 bars.
And as for the second point, if your shouken is blocked, you can FADC.backdash instead to cancel the move and back off and go back to the neutral game(note: some characters can still punish this).
And yes, it’s usually recommended to break down longer chains into smaller bits first.