Alright I watched your first 2 matches.
One thing I noticed, I don't think you EVER used ftilt (actually, once). It's a great spacing tool with decent range. Your utilt use was good though.
MOAR LAZERS.
On stages like battlefield, you need to learn how to apply what I call 'platform pressure'. This is capitalising on the opponent whenever they are on a platform. Falco's nair and bair are very good at this, particularly nair. IIRC, you only applied platform pressure once in the second video.
One thing I've learnt when playing falco is that you shouldn't be expecting gimps. I've lost numerous stocks because I've stayed on the edge too long, or I stuff up the edgeguard because I get a bit greedy. First stock, second match, you tried to hit pit with a laser and paid for it. You also tried to go for numerous bair stage spikes. Edgeguarding is pretty much just free damage for falco, so just hit with that bair or laser while the opponent's recovering and then return to the stage. As falco you should not be expecting gimps, and you don't want to resort to firebird if you mess up.