I'm not too sure if it was matchup inexperience or something else but I picked up on a few things in your first vid:
-off of grabs you seems to not give yourself much time to react to your opponent, when you get a down throw on mario/doc, I like to play more patiently then I would against a spacie, do a wd forward and back if you think hes just gonna tech in place or miss, and use dash wd to cover the roll away from you, if you give yourself a few extra seconds to set yourself up some of those stocks woudlve been taken in a much easier manner. Also there were some points when you were going for chain grabs on doc when you couldve easily killed him off of a up air as you were under him and he was in hit lag, the additional grab is great if you want to get more stage control but its hard to land it at a high percent and you ended up just giving him a free ticket back onstage and he took your stock.
-always mind the cape, your recovery is bad as falcon and mario can exploit the hell out of you if you arent careful, on maps like yoshis or dl I like to use sticky jumping off the wall a good amount to help myself recover, and di'ing his weaker hits up and away on bigger stages to help use your down b and get the jump back
-get really crisp with your instant uairs, make them instant, like on a drop of a hat you can throw it out. Its hard but in both of these matchups your up air has amazing juggling power and can lead into a knee setup very fluidly. This will help you immensly in both your vs doc and vs marth, as both can get stuffed by your instant uair once their grabbed. This is also the same for your knee, if you used the left stick to sh your knee will come out quicker then it would ever if you used y or x to jump, it makes it easier to land almost everything, not too sure if you were doing that but as far as I saw I wasnt seeing it.
Admittedly im not amazing at the vs marth matchup for falcon but I have played the MU a lot with friends and have done a lot of thinking about this matchup:
-The first match something that comes immediately is your third stock you double jumped infront of the marth in perfect sword range and just gave him your stock. You seem to really like running at the marth with nair or using a distance closing move like side b, this is really detrimental, your pretty much serving yourself up to the marth asking him to hit you in the face. I used to play like this all the time when I first started and get mad when I would get 3/4 stocked by my friend who barely plays. Once I started to just sit back and I think more about exploiting the weakness instead of trying to overpower the strengths with pure speed and ferocity. the falcon will do the best here if you play back more, exploiting your movement options and pouncing on the marth when they falter in their spacing or throw out a empty move.
-anytime the marth is above you on a platform or falling onto the stage he should be paying for it by taking a few up airs to the face or worse, I know I said this before but learning the more advanced moves for falcon will pay off down the road as the tech skill that you practice and burn into your memory will be shown in tourny play.
-when you do get a grab on a marth you need to take that as far as you possibly can, in the second match @4:36 you get a d throw on the side of the stage, and this is one of those key points I talked about earlier. here is where you have the opportunity to even the game up, but it seems that instead of either waiting for the marth players reaction or making a hard read that he would tech in place due to where he landed on stage, you went for a dd into a regrab attempt. I think you either go for another jc grab right when you get the first and try to force him into a bad off stage scenario, or you read the tech in place/away and throw out a knee, i think either way you wouldve hit. but when you try this you need to commit to it, the dd that you did in between was the difference between you getting him before he got the nair off and you getting hit. You also couldve waited a second and knee/stomp him off the tech in place, I find that again getting out the super quick knees and upairs in this situations are imperative
-I noticed you seem to throw out your nair pretty wildly, if you start using it in a more controlled manner youll start getting way more opportunities to take a stock. i've always seen the nair as the nutcracker in the tool kit of falcon against marth, you can use the single hit nair to get some easy percent in sure but what it really does great is disrupt the wall of pain marth is trying to throw up against you and give you the second or two needed to get the grab off and start the combo or use a side b as a mix up if you have been using single hit nair into grab as a approach a lot, varying up is great. and speaking of variance the nair has a fucking amazing second hit that really opens marth up and exposes his issue of getting out of combos, the knockback from the second hit of nair can almost combo into any of your aerials if im not mistaken at higher percents, and works amazing at low % at opening marth for a easy grab or even throwing out a knee off reacting to his tech.
-tech chase with stomp against marth at 60-80% for the stomp knee kill combo
Its really late now so im gonna stop here but I think I gave you some good general tips and a few specifics to back up my point.