This is a great idea and it looks like it might work fine with comp tf2. Here's my feedback to you:
Add applicants available weekdays and hours to do team stuff, this is important in many ways, for instance, to figure out how often you can expect the player to be online and if its a player that wants to practice many times a week or just looking for a chill team.
Let the applicants expand on past experience, hopefully in what teams they played before, including team league and division with links to the league's team profile page.
Comments and references are important if it's an experienced player.
You don't have to go through trouble on server space for demos, make ppl upload their demos somewhere else and post the link to it.
As for the youtube videos, I don't think they're important at all (at least I wouldn't look at them very seriously). Unless its a full POV making amazing plays through a whole pug/scrim/match, youtube videos usually show a very cool killstreak of someone playing well, but we've all had one of those moments and it doesn't really mean that you're good, it might have been luck or shitty enemys or w/e. So I would let the youtube videos as a thing that the applicants can put on their applications as an extra, but I'd remove the "Search Only Applications Containing Youtube Videos" option on the search page.
"Include Free to Play": this is just unnecesary, if someone really thinks that everybody who joined the game after Jun 2011 is automatically bad, then you shouldn't be forming a team in the first place.