can I use MainStage instruments/patches in studio one?

Nope. MainStage instruments are built-in to the app and the settings are only supported by Apple's products Logic, MainStage and in some circumstances GarageBand. MainStage does received MIDI via IAC (inter-application communication) available via the Audio MIDI Setup. You can either record the output inside of MainStage and import it to other DAWs or, you can use something like SoundFlower to route the output of MainStage into another app like Studio One. (this may or may not work well for you)

Or, for $199, you can switch to Logic Pro X which is fully compatible with MainStage plug-ins, instruments, patches, etc. It contains the same sound library and plug-in set as MainStage. It can also output stems of your tracks which can be imported into Pro Tools, Studio One, etc.

No.

MMainStage records stereo out. Press record button on tool Bar.