Yes, there are many free-to-play games available online.
Yes, there are many free-to-play games available online.
TF2 isn't quite P2W, though you can upgrade to Premium for just $0.10. Robocraft is a bit closer to P2W, and Warthunder World of Tanks was enjoyable during its early days, though it's quite intense.
I enjoy Planetside 2, though the learning process can be tough. You're immediately dropped into challenging gameplay with tons of in-game time right after finishing the tutorial. Later, they introduce a new area for newcomers to grasp the mechanics—just give it some time and stay persistent. With effort you'll improve.