I use several of this motors (600w and 750w for motion control and 3.8kW one as servo spindle). What you are experiencing is not normal. Mines use the A1-SVD drives, not the AASD, but they seem to be the same as the manual and all parameters are equal.
Lets start with your last questions.
-The manual states that the maximum input pulse frequency is 550kHz for diferential input (and encoder input) and 200kHz for single ended. With 500kHz your motor (with 2500 lines encoder) turn at maximum speed wihtout the need of any electronic gearing (Pn098=1, Pn102=1). If I remember right, I have 800ns as step lengh and step space, but redoing the math it should be 900.
-With your drive in speed or torque mode, it does only uses the +/-10V input. Your Mesa board don't have +/-10V signal but you can use your drive in position mode, there is no problem on that. This is how I work on my lathe, since I have a 7i96s. The pncconf utility does use velocity mode even to motion control. Your board will send the driver pulses at the right frequency and it should follow the speed command without problem. At startup and stop it will not follow the right speed as it will try to follow the position, but you can put some acceleration and deceleration ramps in linuxcnc. I haven't programmed them yet on my lathe and it does work with the 160mm chuck, so on your spindle should not be needed either.
-It's werid that you get to move your motor well unatached but not with the belt, given than the load is quite small. Is the belt well tensioned? Does it spin freely? Sounds like a mechanical issue.
-How have you performed your load-intertia ratio estimation? First you have to calculate the inertia ratio between your motor and your load (motor pulley and complete spindle) and introduce it on Pn266 before executing the Fn018. The spindle must be also engaged. I have found that the inertia ratio calculated by the autotune (inserted into Pn257) is not the one that give me the best sharp movements (at least for position control). I use it as reference but I tweek it up and down to get a faster response with the higher rigid grade selection (Pn259, usually 6 to

I can set.
-Have you programmed the right motor on Pn001?
-The AL-04 is probably overheating of your drive caused by the sudden stop of the motor after several test. The energy of the motor is dissipated on the internal breaking resistor and it will get hot. Since you are probably testing the motor with many start and stops, it will accumulate heat and the driver will enter on that alarm until it cools back. Either program on linuxcnc the deceleration ramp or use an external resistor.
-For the queston of besriworld about the pid settings: if he is using automatic gain adjustment (Pn258=1), all those PID parameters (Pn115,116,153 to 156, 196 and 197) are not used. All are overrun but the rigid grade selected on Pn259. If the drive is set to manual adjustment because he needs better response (for spindle use I don't think so), then he could tweek those paremeters.
-I have no idea why you have set Pn275 = 1.20. This parameter is for internal use and is not described in the manual. Also leave Pn020=0 and set the correct Pn001, the manual says not to modify the Pn020 for general use as it does affect other parameters.
Since you have tweeked several parameters, I would set to factory the drive and start over again.