I seem to have terrible timing when trying to reflect rockets, pipes, and arrows. What is the timing that I need to use to reliably reflect these? Is it right before they hit me, or is it further out? Does the distance the projectile is from me matter? Or is the determining factor the amount of time it takes to hit me? (Since DH rockets and arrows are faster than standard rockets, there's a difference between time and distance.) Does lag compensation affect this?
The compression blast range appears to be slightly shorter than the range of your actual flamethrower, from personal experience. You can compression them anywhere within that range and you'll reflect. The angle that it gets reflected back at is dependent on where your cross-hairs are aimed when you hit the compression blast.
Additionally, for grenades, there appears to be some determining factor with return velocity depending on your distance from them. I can't find a lot of info about that though.
Rockets will travel indefinitely until they hit an object. Arrows seem to function similarly to grenades, but less noticeably so due to their natural high speed and lack of "bounce".
In regards to lag compensation, the compression blast is NOT lag compensated. You're going to have a harder time reflecting rockets / grenades / arrows if your lag is higher, especially when dealing with the higher velocity ones like the Direct Hit rockets and arrows.
Edit: As per the link in the comments, edited the above to indicate that the compression blast is NOT lag compensated.
It's hard to say "when" you should compression blast. It's a function of distance and velocity, rather than time from fire. With any projectile, it's nearly impossible to reflect at short range without some sort of luck / godly reaction speed. At longer distances, the Direct Hit and arrows can still be relatively difficult to reflect. Again, it's about the distance, not the time before it hits. The best way to get a feel for it is to play it and learn it intrinsically, not go by a paradigm that there's a hard rule for timing it based on seconds.
There is a narrow band of space in which things must be reflected. Obviously faster projectiles spend less time in that space and therefore are harder to deflect. Also which way you're aiming matters, which you can use to redirect rockets at other targets ... or at your feet to rocket jump (just remember to jump). This video should be helpful, and there are several good maps for training offline. I prefer TR_Walkway (video). I would guess the distance is between 1 and 3 meters, though confirmation would be great.
When you are medium/close to an enemy, try to think about when he is going to shoot, and pay close attention to where he is aiming. This primarily applies to soldiers.
Most soldiers will tend to fire their shots close together, and in a regular rhythm around one second apart. Try to predict the moment he will fire based on that rhythm and how he is lining up his aim on you.
This is definitely a more advanced technique.