Tracer's key strength is her mobility and hard-to-predict movement patterns. However, she is very fragile and if she is caught out, she will die. Also, while she does well at fighting 1v1, she does very poorly against a grouped team (unless she manages to stick her ult).
Tank-wise, Reinhardt is a good option as his barrier doesn't allow her to build up ultimate charge and forces her to attack you from the sides. By narrowing her avenues of approach, your allies can cover your flanks. Winston is also a good choice. Although his shield is stationary (unless you place it on the payload), his weapon fires in a cone which allows him to track her much easier.
Heroes with CC are also helpful against Tracer. McCree's flashbang can stun a flanking Tracer, allowing him to pick her off with ease. Mei's Endothermic Blaster does the same, although it requires locking on to Tracer for 2 seconds. Junkrat's Steel Trap can root Tracer, but it's an immobile trap. While Roadhog can hook a Tracer for an easy kill, his large HP pool and hitbox make him an easy target for ultimate charge.
Situationally, S:76 can be useful although risky given the aiming needed to connect with his heavy pulse rifle. However, his ultimate counters Tracer very handily given that he'll automatically target her no matter how she dodges unless she makes it out of line-of-sight. Pharah is also a situational pick. Tracer's Pulse Pistols have heavy damage falloff and Pharah is usually high up enough in the air where Tracer can do little damage to her. While Pharah is also not as likely to hit Tracer with her rockets if she's paying attention, most Tracers won't be looking up as she attempts to flank your teammates.
Torbjorn is also deadly to a Tracer because his turret auto-locks onto her and her damage falloff prevents her from taking it out at range.
No. Shields absorb enemy projectiles from both sides. Likewise, allies can fire through it from both sides. That is, the team the shield belongs to determines whether projectiles pass through it.
My only source is primary: approximately 150 hours of play, much of it as Reinhardt.
Best Answer
As mentioned in the comments, Hanzo's wallhack is answered in this question. As for Widowmaker, it is possible to hear her say "Personne n'échappe à mon regard", which is French for "No one can hide from my sight", but it's very quiet compared to other ultimates like Barrage, Tactical Visor, or Rip-Tire.