First time going to GenCon. Will we be able to playtest new games? Does that cost anything? 

There is something called the First Exposure Playtest Hall.  For the cost of a generic ticket ($2), you get 2 hours playtesting new games.  It runs from about 8am - 10pm every day (probably to 4pm on Sunday), so you can run it multiple times and try out a bunch of new stuff.

There is also a new/indie games area, where again, for a generic, you can play stuff from small developers & just released games.  Companies may be demoing in-development games at their booths, and they have many free events demoing/playing just-released games.

From what I understand, Pathfinder 2.0 is still in development (the playtest for it was released at last year's Gen Con), so I'm sure they'll be running plenty of events with the new rules.  Since I don't play PF, this may be incorrect; someone with more knowledge could provide better info.

Companies that have paid for space - either a booth in the exhibit hall or a full-time table in a gaming hall - can use that space to run free demos of the games they want to sell to you. Additionally, many companies run games as ticketed events. Those are usually $2.

Take a look at last year's event list to see all the games that were offered at what prices. And look at last year's map to get a good idea of which companies are there.

Buffythecatslayer is incorrect. The First Exposure Playtest Hall is free for players. The game developers pay for the use of the players to test their games.

Also, the dealer's hall is HUGE. You could spend a day (closes at 6) playing demo games at the various booths. Some have full games, some have partial demo games and a few just teach enough so you understand game play.

Playing new games in the events list is fairly cheap unless you sign up for "play with a celebrity" events; those run $130 last year. There is also a games library but that won't have other people to teach you the games. You just check those out like library books.

I must have it confused with another event, maybe one of the new/indie games ones, where registration is free, but they collect generics at the door.  Even better for the OP.

Actually, First Exposure Playtest Hall players do not pay to play, not even a generic, players (playtesters) play for free.

There are lots and lots of demos in the exhibit hall- I haven't tried, but I wouldn't be surprised if you could basically demo constantly from 10-6 each day if you so desired. Some of the demos will be full games, some will be just a few sample turns, it depends on the game and company running it. Sometimes the games are already released or a new release, and sometimes you are playing a mock up version for a game that's not out yet. A few of the bigger/more popular games might have a waiting period or even a sign up list for demoing. Pretty much all the demos in the exhibit hall don't cost anything more than your badge. 

If you're socially bold, you can also just wander around areas where games are being played and ask to join in one being set up that interests you. These might be a ticketed event, or they might not have room, but sometimes it's just some friends playing a game and they're fine with an extra player. Even if the answer is no, 99% of people will be nice about it. My friends and I have played many games with some random stranger who just asked to join us. We've also seen the random stranger ask to join, then retreat when the 60 page boardgame rulebook came out. To each their own. 

I have had a blast every time in the First Exposure playtest hall. The biggest difference between that and the demo hall is 1) you have considerably more time to have the game and rules explained and 2) the noise level is much less. I also enjoyed that you picked the 'type' of game you wanted to demo, and then afterwards, a real chance to give feedback to the developer. Even when I GM 32 hours I make time to squeeze in a round here--so much fun.

And hey, even if someday I run into a game I don't like, I'll know before buying--OR can actually explain WHY I didn't like it and maybe it'd get changed!

You can preregister for a time, in which case you get precedence over the other option, which is show up when YOU have time and if they can get you into a demo, they will and do.

We did one session in the FEPH last year. I didn't enjoy it as much. Mostly because I felt like we were then to give input to the designer and when the time came, the designer shrugged our comments off. It was discouraging, because while yes we are gaming, we are giving our time to try and help the designer. And he clearly did not value our time. This is nothing against the FEPH, but we will probably not go back. There is plenty of other options. We prefer the BGG Hot Games Room.

If you were giving constructive feedback (i.e. "this game blows!" is not constructive :-) ), and the dev was shrugging it off, then his loss, and his hundreds of $$ wasted on the FEPH.  Don't let one guy turn you off to the concept.

The Hot Games Room is good too, but those are games that are already out.  The OP was looking to playtest, which implies pre-release.  Still, it's another good option to try something new, that may not yet have gone wide.

Buffythecatslayer is incorrect. The First Exposure Playtest Hall is free for players. The game developers pay for the use of the players to test their games.

There are a total of 27 playtest slots, and they are all free - join us for as many as you'd like throughout Gen Con 2019!