1. Most of the trig functions are limited to PI/2 to -PI/2(eg 180 degrees total, +-90degrees)). You will need to rotate your angles to this range, use the function, and then adjust the result if necessary.
2. Very intensive. No the AtomPro does not have a math chip. No processor I'm aware of in this class range has a math coprocessor or FPU. The AtomPro does have hardware multiply and divides which help plus it does math in 32bit chunks which also helps. In the end it much faster than an Atom or BS2 or PicAXE or PICmicro when it comes to FP but it is still pretty slow. You will see 1k to 2k FP calculations per second when using the trig functions.
3. TOINT and TOFLOAT are not very intensive. They are basically just some bit shifts to convert from an integer to an fp to an integer. Compared to most FP functions they are blazing.

4. If you don't need high precision you can use the integer sin and cos functions. These are very low precision since they are 8bit integers representing the values. ANother option is creating lookup tables for specific trig functions. You can make these as small or large as you want, larger having better precision. Then it's just a matter of grabbing a value from the table(eg very fast). THe down side is for high precision you have to create large tables which a) is a pain in the ass and b) takes up flash memory you may want for your actual program.
Just as an example, I've used FP trig functions in several IK routines for hexapod robots and 5 and 6 DOF arm robots. They run very smooth and fast enough I couldn't see any significant slow down compared to integer versions done by other people.