I won 1st in the FTP 2700-player $100 Freeroll once.
Truth be told, solid play will usually always get you deep in a tourney, but, of course, luck will always play a key role in getting you those key pots.
That being said, I think you're asking two things, and I'll rehash what I'm interpreting, in my own words.
First question was, "How do I avoid getting sucked out when the UTG open raises all-in with 3c6c and I call with QcQs"?
Unfortunately, you can't help it. Matter of fact, I don't think you could depend on a "non-donk" shove pre-flop until about 15%-25% of your competition has been knocked out of the tournament. For example, if you're in a tournament with 2700 players, somewhere between 400-675 of these players don't have a damn clue what they're doing, and would take any suited cards vs. an overpair any time of the day. And, as the game of poker has it, these monster suck outs can, do, and will happen. If you don't want to take the chances of falling victim to these gamblers (read: crapshooters), you have the option of tightening up your game until these 675 or so players are out of the tourney.
So, don't go all-in pre flop at these stages unless you a)Have a bonafide MONSTER, b)Are all-in with nothing more than 2-3 other villains, the less the better. I would recommend calling an all-in from late position, so that you have a better look at what you're up against. Last thing you want is to call an UTG all-in from early position and find the CO, SB, and BB call the all in with you. Obviously, the more players in with you, the more volatile your chances.
Second question was: "How do I get in the money."
Well, that question in itself is interesting. Any player could have their own mindmap set up as to what style would be the most profitable in a *ahem* freeroll tournament. Some could argue that the Tight-Aggressive style is what will get you to cash, others would prefer the Loose-Aggressive, stealing pots and bullying the table to gain, and build on, an early lead. So as far as playing style goes, I would say, go with what is the most profitable for you at the table you're at, whether to chip up, or to defend yourself from losing chips from a maniac who you just know is going to raise you 5 BB's on the flop regardless. But do note that it's very important that you are able and capable of switching gears, as well as identifying and adjusting to your opponents, as you will be switching tables constantly, so to know how to exploit every style of player.
Secondly, picking your spots is a priceless skill to master. One of the biggest mistakes that newer players tend to make, is that they give up too early in a tournament when they're short stacked, even though they still have 20 BB's. They start making bad decisions, and hit the panic button when they're still in the top 80% really early in the tournament. Stay patient, especially early in the tournament. The FTP 2700 person freeroll usually lasts about 5 hours. So, if you're not in mid-position on the leader boards by the first hour, just remember to put it in perspective. You're usually still good if you're still in the tournament with an average stack by the first hour.
Third, and this, just a bias, because it's a lesson that I'm still working on and am seeing to be very valuable: Think harder and deeper about your hand play than you ever have. CardPlayer magazine has segments of hand analyses' where pro players walk you through their thought processes on certain hands and why they played that hand the way they did, even if they didn't have the best hand. The best way to get deep in a tourney and getting in the cash is to be the cream of the crop. And the cream of the crop will always
have an edge over other players. I'll throw out some subjects, all of which (plus others not mentioned), you'll really need to know, and instinctually be able to execute consistently, and implement into your game. Along with the other two points, this point being the most important:
*Reads and Tells
*Continuation Bets... how, when and when not to do it.
With that third point being said, understand the luck factor in freeroll tournaments, and understand that winning a freeroll may possibly be a false gauge as to how good a player you really are. And this is because not everybody in a freeroll actually plays like a poker player. But, if you take those 3 points into consideration, I think you won't necessarily get in the money all the time in a freeroll, but you definitely will have an edge.
Good luck at the tables.