Hello,
1) If you want to use SPE, there is option for Signal Processing in project properties. Please see the figure below:

2) S32DS project uses VLE by default. There is no additional option to enable VLE.
3) I am not sure, what do you mean by APU. Only thing I found is APU exception in e200z7 core, but this is not supported by this core. If you mean Auxiliary processing unit then this unit is not presented, but this functionality is included in EIS. For more information, please see Core reference manual.
https://www.nxp.com/docs/en/reference-manual/e200z760RM.pdf
4) You can use Hardware Vector mode instead of software vector mode. Please see chapter 7 in core reference manual and chapter 15.5 in MPC5777C reference manual.
https://www.nxp.com/docs/en/reference-manual/MPC5777CRM.pdf
Please see also example project, which was created for MPC5646R, which is predecessor of MPC5777C.
Example MPC5676R HardwareVectorMode Multicore S32DS
5) Usage of floating point can be enabled by Use hardware floating point option in Project properties.

Hope it helps.
Regards,
Martin