I'm not sure if I understand your question: Are you trying to use all of those instruments simultaneously, or just want to know how to set up your midi controller to work with Studio One, so you can control those three instruments separately?
To set up your controller, you need to go to Studio One > Options > External Devices and set it up as a new keyboard. You might possibly get away with using the AKAI preset for the MPK49/61/88. You might have to refer to the Akai Mini MK2 manual if there are any specific settings to map the drum pads and knobs to the right notes / control change numbers, but this preset might be a good start.I've attached a picture of the settings page and the relevant example
Following that, simply insert Impact XT, Mai Tai and Analog Lab 4 onto separate tracks. If you want them to sound simultaneously, you'll need to click on the input 'monitor' button on each track (highlighted in red). Where my picture has 'Komplete Kontrol S61' you'll need to see your AKAI device name there. The pads on the AKAI mini mk2 will have to be mapped to the Impact XT pads you want to use. However, I don't think you'll be able to play the pads independently of the Mai Tai and Analog Lab Synths, since there is no way to limit the keyboard ranges in those two instruments.
Apologies if this wasn't what you were asking, but hope its of use all the same