I can see that you and your top tier playing friend could both use some tips and all, falco on spacing and playing smarter (gotta learn not not get shieldgrabbed after lasers lol, spacing man), but I'll touch on the peach stuff as of now.
Against falco:
First of all, do not edgeguard with upsmash. Only when you have no other option on punishing a falco/fox using forward b on stage and even then there are better options. Weak upsmash combos sure, but especially on your situation simple float over there and butt the falco would've been a much more efficent choice and would have KO'ed him. So do not be shy on reaching falco. Unlike fox, falco lacks a hitbox on his firebird loading animation, so you can hit him with whatever you wish. Turnips into edgeguard/hog are especially good. So work more on your edgeguarding and make it more efficent and deadly, float over their faces and butt/nair or stuff, edgeguard on stage with aerials like spaced fair or even forward smash or aim a turnip on their face from various directions. And when you see they cannot make it back to the stage anymore, don't bother edgeguarding but just float backwards to the ledge and drop down to edgehog, then time your rise up so you don't get hit.
Secondly, work more on your chaingrabbing skills. Uthrow to dsmash works well from zero and bit higher % and after that cg through the stage is good. Dash attack also works very well against fast fallers and in tandem with basically every float cancel you do, so use it more. You need to follow more aggressively when you see an opening, so you get in consecutive hits and build up damage faster. Some more dsmashing also doesn't hurt. I see that you also use wavedash as one form of movement, so what you can do against falco is wavedash from shield to various stuff, which works like a dream. Wavedash back as falco tries to use dair, with good distance, makes em open for some good dsmashing or chaingrabs or whatever you may wish to use. Same goes for dash dancing.
Thirdly, you need to watch more closely what your opponent does. If he retreats, dont mindlessly attack him without a plan to actually hit him. If he lasers, don't stand there but shield it, float over it, powershield, sidestep it... if he jumps and is on top of you, don't stand idle either but move out of the way or shield it, there is little chance he'll come down with anything else than a dair. So you need to plan your movement beforehand and watch what your opponent is doing, not just float cancel and hope for the best or do some other unneccesary movement.
Fourth, you need to lay low on grabbing from shield all the time, that reflexive action will hurt you on the long run. Work instead on different kind of maneuvers, aforementioned wd from shield will move you into more safer position but allows you to punish your opponents action. Float cancel/aerial from shield is instant punishment, while rolling is just to get away quickly when you don't see an opening or are unsure what to do.
To sum it up: Edgeguard more effectively, work on chaingrabbing, consecutive hits and real combos, pay more attention to your opponent and plan accordingly aka play smarter and finally work yourself out of the shieldgrab habit and test out other options.
Getting more technical and better timing never hurts either. Also watching other good peaches play like cort, armada and pc chris for example never hurts either. I've personally found japanese peaches like mikael, kei and ikki really educational when I started playing peach, same with vidjo, azen and edrees. Throw in some wife, ryoko, bone, rock (mexican) and sastopher. If you understand why players make the choices they make and why it works, you understand the game itself and can work from that. Playing smart is important, but understanding why an action is smart is the first step to playing smart yourself and getting good on smash.
