All of the above is good advice.
You can also use denatured alcohol to remove Tamiya acrylics. It will remove the paint very quickly, with no effect on the styrene.
If your paint is running, it's more likely to be either too much trigger (paint flow) and/or too high an air pressure at too close a distance.
What are you using as an air source? If you are using a compressor, for a siphon feed brush like the Crescendo, I'd suggest about 15-18 PSI and work from there. Go much below that range and you may have problems with paint "draw" from the jar and perhaps reduced atomisation, causing spatter. If you're using "canned air", it will be difficult to regulate the pressure and you will need to concentrate on regulating the paint flow using the trigger.
I doubt that your paint is too thin. I often airbrush Tamiya acrylics up to 75-80% thinner to 25-20% paint. Tamiya paints have a fairly high pigment load and can be thinned quite considerably. The key is to apply multiple thinly applied coats. Never try to achieve "one pass" coverage.
Oh, and PLEASE, tell me you're not thinning with water. In very small amounts, it's ok, but more than about 10% and you will be breaking it down, leading to poor adhesion and a chalky finish.