Honestly, I wouldn't try to solder my own BGA's. I know this doesn't directly address your issues, but hear me out.
It takes a lot of work and effort to solder a BGA. There's a lot of trial and error. A lot of messed up test boards. But then it's soldered. Now what?
Now you have to prove that it's soldered correctly. For that you need one or more of the following: JTAG test (US$10k, never has 100% coverage), optical inspection (US$20k for the equipment), or X-Rays (US$500k). The cost of doing these tests is too much for the normal hobbyist, and is even beyond many small companies.
Skipping those tests, you proceed with debugging your PCB. And let's say that the BGA is a complex CPU. Inevitably you'll find a bug. The CPU will randomly crash. Is it your software, your electrical design, or the soldering on the BGA that's causing the problem? Debugging this, in light of some possibly problematic soldering, is going to be terrible. It will add a lot of time to your debug process, possibly months, and you'll loose a lot of hair on your head. And then you can repeat this for the next major bug.
Without confidence that your soldering is perfect, you will always have this dark cloud over your head. Every little bug that shows up "could be a BGA soldering problem". This is made worse if you have multiple engineers working on the same PCB since the software guy will be questioning the hardware guy, etc.
Then, even if the BGA soldering is perfect, did the chip get too hot? Did you destroy the chip by getting it too hot? Even on modern assembly lines this is an issue. But with the proper equipment you can adjust and measure the temperature profiles to at least get you in the right ballpark. On one board I did recently, the BGA's were being damaged. The solder balls looked great, but under a very nice X-Ray machine we could see that the gold bond wires melted from the heat.
I've been there. Not at the hobbiest level, but professionally as we were bringing up new boards while the assembly shop was learning to do BGA's. We had no JTag. No optical inspection. And the X-Rays were terrible. Our PCB had 11 BGA's on them. That was 2 years of hell I don't wish to repeat.
So, here's my recommendation:
Get someone who has the proper equipment, training, and experience to solder your BGA's. There are a lot of contract manufacturers that'll do a single BGA. It takes money, but that's way less than the time you'll spend trying to debug your own soldering.
If you must do it yourself, then you should get the proper equipment, training, and figure out how to get the experience required. For this to pay off in the end, you need to have a large enough company and need to justify the huge amount of time and money that you'll put into this.
But I would never try to just kludge something together. That's a recipe for, um, bad stuff.
Very good idea to practice, practice, and practice some more on salvaged boards until you get competent with new tools. You didn't notice the solder had reached the molten state because there's so little of it used to solder components.
The typical lead-free solder has a melting point around 217 degrees C, so you'll have to get the leads and pads up to that temperature before trying to remove the component. The reason why you need a much higher temperature is because you want to get the solder joints to the melting point as fast as possible. If the hot-air gun is set to a much lower temperature, it'll take a longer time to reach the melting point. The longer the time to raise the temperature of the leads/pads will increase the overall temperature of the component, possibly past the point of destruction. So the technique is to heat it up fast, remove the part and hot-air gun, then put the part where it can cool off.
Now, if you're removing a part that's already fried due to some other reason, no worries then. Just don't damage the board by overheating the pads and causing them to lift off. If that happens, your headaches are just beginning on this repair.
Best Answer
I know this answer is a bit late ;>) but hopefully it will help others who search for something similar...
The goal when manually reworking circuit boards is to apply the right amount of heat. If there are lots of adjacent SMD passives, especially in smaller 01005 packages, then lower air flow is preferred otherwise you will have a mess on your hands. However, if you have to deal with a larger IC or a large ground plane, then more airflow will certainly help. Personally, I primarily use 360-380C with low airflow.
If you leave the heat on too long, eventually the circuit board will get hot enough to melt solder way beyond the area you are reworking and that will cause all kinds of damage. If you are seeing components being affected on the opposite side of the board, then you are applying too much heat.