FALCO
Falco's magic number is not 159% at the start of the throw on FD; it is 172% with perfect DI.
OFFENSE
Falco is a dirty bird. Powershield > Wavedash > Down Tilt/Grab is the best way to get through SHL on any stage. I usually just teleport into Falco with my shield up and invade his SHL space, the space where he can SHL comfortably while standing still, and follow him if he tries to retreat his SHL or read for a SHFFL cross up from Falco by doing a quick pivot shield reading for shield grab or a quick retreat.
It's also good to do a forward baby shadow ball at Falco when you know he's going to retreat SHL, then follow that up with your wavedash down tilt or grab.
COMBOS
The most consistent combo I've found on Falco on FD for the left or right DIed up throw is grab > up throw > Full hop but you DJC your forward air near the apex of the jump so you fall with the forward air > JC grab either direction he decides to DI > up throw > forward air to up air or to confusion for an extended tech chase.
If the Falco doesn't DI your up throw at 0-6% straight left or right, then the usual double forward airs to whatever **** combo you want works pretty well. The only hard part is if they don't DI the throw but they DI the forward air behind you, so you just have to know before hand to throw your forward air while floating backwards to continue the combo.
I have some good footage of what I'm talking about in Shadow Claw 3.
DEFENSE
Disable out of shield works pretty well if they try to do a jab/tilt approach to you, as well as shadow balls and well timed SH neutral airs. Teleport out of shield and wavedash out of shield to avoid the SHL rush down pressure, light shield/wavedash/jump and retreat to the edge to refresh your shield and to even bait the Falco in to approaching you. If the Falco bites and invades your space by the ledge, you can easily turn the tables with a simple ledge hop teleport and move back into him with your shield up and Falco no longer has much space, so his options become panic SHFFL aerial or grab, and you can compensate for both of those with good spacing.
Falco’s SHFFL N-air > Shine > grab/Shine are probably the main things that will throw you off from good Falcos. You have to be ready to retreat/shield grab if you know it is coming. Sometimes you’ll be forced to play a high and floaty game above Falco until you figure out their ground game, and falling neutral airs to tech chases may be all you have.
EDGEGUARDS
If up throw won't kill or combo, just don't do it. If your back is to the stage, down throw. If your back is to the edge, back throw. Down Smash is a perfectly fine edgeguard against Falco's Forward B if you have an ounce of timing, because it isn't laggy either. Down tilt can be ok, but usually at higher percentages, not lower. I’d use down tilt to combo into a KOing Forward air, down air, or forward tilt. Also, it just doesn’t feel as potent of an attack as Down Smash for hitting people under the stage since the attack isn’t disjointed.
When you're edge guarding Falco, just think what would Marth do? Then you do it. Take the ledge, force the high forward B, if they don't then they have to Up B and then you just back air them away. If they up B higher, go for the back air anyway and chase them far enough that you can barely recover with teleport and Falco shouldn't be able to make it back with his Up B. You want to control as many options as you can, so when Falco is trying to recover, throw Shadow balls where Falco has to B to drop him a little lower, force him to Forward B sweet spot and punish it by down smash or taking his Cookies, Ultra Ninja style.
OVERALL
To beat Falco you have to fight and fight to get Falco on his back then you cling on to him like fly on ****. Keep tech chasing him, tracking him down with your shadow ball wave dashes, keep throwing him off the stage and threatening his recovery. Falco can't really kill Mewtwo easily; he can just build damage until about 130-140% where you start dying from sweet spotted aerials. Forward Smash and down airs might kill you earlier, but those things are avoidable. If you can break into Falco's rhythm and keep him from controlling you with laser spam and spaced tilts/aerials, then you'll win the match.