BlackSheep,
Tamiya is a hybrid acrylic, I've had luck thinning it with a mix of - 30% 70 USP isopropyl alcohol with 70% distilled water, I use this same mix for Model Master acrylics. I know a lot of folks swear by the brand name thinners. I also know you do not use alcohol for Vallejo acrylics, only water. I use Windex to clean airbrush parts after spraying acrylics, or to remove acrylic paint. It contains ammonia, which will remove the acrylic paint. Another acrylic thinner a lot of folks use is Future (Pledge floor protector with 'Future Shine'). I've not tried this.
Thinning ratios are another consideration, and difficult to put a formula to. The goal is 'the consistency of 2% milk'. I use bottles that emit a drop at a time, and slowly add my reducer stirring with a toothpick in the paint cup or separate bottle. When I have the paint no longer forming a drop on the end of my toothpick, but leaving a thin coating on the toothpick (i.e. not dropping off) I spray. Now you have to watch your air pressure and trigger. It's practice.
For enamels, I use Tamiya lacquer thinner for reduction, and hardware store lacquer thinner for cleaning airbrush parts. The hardware store stuff is much 'hotter' and for this reason I don't use it for reduction or stripping paint. Especially stripping paint, it will melt and even destroy styrene.
If I am doing shots of different colors in one session, I run the reducer (thinner) through the brush between colors. I keep shooting until I'm getting only clear reducer out. I've personally got an Aztek brush, so I can quickly change the nozzles if one gets choked up (I mostly shoot acrylics).
After each session, I soak my nozzles and paint cup in Windex, and using bottle brushes, toothpicks and q-tips I hand scrub the parts back to clean. You have to be very careful with needles, you don't want to bend them, and they can be one of the dirtiest parts. If using enamels, I use the same with the aforementioned lacquer thinner. The best way I've found to clean feed cups is to soak in the reducer and wipe out with a q-tip. The toothpicks work well for getting inside the nozzle, as do bottle brushes. I personally wipe needles VERY CAREFULLY with a tissue or paper towel, towards the point.
Also, you don't want to soak the whole airbrush in the lacquer thinner, especially the hardware store stuff, it will eat out any teflon or rubber inside.
A great investment, depending on your budget and the justification for the amount of use, is an ultrasonic cleaner. Using water or a soapy water mix, you drop all the parts in the cleaner and let it buzz away. The sound waves traveling through the water knock all the gunk off the parts. Again, you don't want to use anything flammable in the ultrasonic bath. Little jewelry cleaners aren't expensive, but you do have to get a good one (I started with a cheap one from Walmart, and you get what you pay for).
I hope this helps you. There's a lot to learn about airbrushing and care, and a lot of good videos on the net if you Google airbrush care or cleaning.