EX Red Dash into Up/Down Slash to counter projectiles (for some of the slower ones you can just use teleport, or outzone them). Also can be used to counter pressure similar to Sonya's EX Cartwheel. EX Red Dash, Red Slide can also be used to get the first hit in the match but it's risky if you mistime it.
Whenever you land a blocked jump-in go for her F2, 1, 2, 1+2 string. If the oppoennt is stand blocking at the end of a blockstring you can use EX Dagger Toss and dash cancel into another blockstring (another F2, 1, 2, 1+2 should connect iirc).
Ending combos with 1, 1, 2 you can go for Red Dash into mix-up (Slide/Throw/Down Slash). Down Slash is very risky though and is like Sub-Zero's F4 so use Slide and Throw as a mix-up. You can also use EX Dagger Toss after 1, 1, 2 and dash cancel into F2, 1, 2, 1+2 blockstring.
Down Dagger can be used to hit opponents trying to poke you or you can use it to fake jump-ins. Don't use it too much as it can be very predictable and can be punished.
Down Dagger or Dagger Toss (dash cancel) on hit from dash distance stuns the opponent long enough for you to move in for a blockstring.
Dagger Toss (dash cancel) into Red Dash, Red Slide is another great tactic that can catch the opponent off guard. Or you can use a naked Red Dash to close the distance. Instant Air Dagger is great and fast too but hard to do consistently.
Dagger Toss (dash cancel) to bait opponent's projectile then use EX Red Dash, Up/Down Slash is a great advice from Ninj.
If the opponent attempts to jump over your Dagger you can backwards dash cancel into F4, 3 anti-air or another anti-air.
Non-dash cancelled Dagger Toss is also good since it is 2 projectiles. I have been able to stop Ermac's Lift/Push and Scorpion's EX Spear because the 2nd Dagger interrupts them.
D4, Red Dash can lead to her mix-up game without having to use 1, 1, 2. The opponent cannot poke out or jump out of D4, Red Dash, Red Slide so he must block. Once the opponent knows he has to block, you can start adding in naked Red Dash into Throw.
D4 can pick the opponent back up from the ground just like a D3. This is unique to Skarlet (and Jade) and lets you go for her D4, Red Dash mix-up game.
F4, 3 is very good. It's safe on block and sort of safe on whiff. It has 2 hits and is probably her most reliable anti-air. It can also stop some opponent's non-armored wake-up attacks. Also good to keep the opponent in the corner knowing that he can't jump out safely.
U3, U3, Air Dagger, dash, 2, 3, Dagger Toss (or Red Dash, Up Slash), dash, 2, 3, Red Dash, Red Slide is her BnB punisher for blocked teleports. It does 42% if you use Dagger Toss version or 44% if you use Red Dash, Up Slash version which is harder to do.
For punishing other stuff, use F4, Red Dash, Down Slash into one of her Down Slash BnBs. Also something to note is that 2, 3 is her highest damaging string in a combo. This is why most of her BnBs end with 2, 3, Red Dash, Red Slide.
B1, 1, F4 is used in her wall combos, which you can see in Ninj's Post-patch Combos thread. UsedForGlue's Skarlet breakdown is also something you might want to check out.
