I cannot speak to whether the CT100 will be able to act as a bridge for your minisplit but I would venture to say not without writing some custom code, there may be a way to actually control the current thermostat you have with ST with some custom code since it does have control through a phone app, the question is whether or not the thermostat will allow you to talk to it via some API that is not proprietary which it really sounds like it is so not sure how much luck you will have there. You may want to look at the below thread regarding the thermostat.
As far as humidity sensors there are a few out there but the only one I can provide information on is the Aeotec multisensor that has motion, humidity, LUX, and temp sensors as well, it is a bit pricey but if you also need motion sensing in the same area then it makes it worth it. Below is a link to that on Amazon although if you only need humidity I am sure there are some other sensors that are less expensive. I have found the sensor to be very reliable and it comes with a cable so you can plug it in instead of running on batteries if you want (it also has batteries if you prefer that).
http://www.amazon.com/MultiSensor-ZW100-Aeotec-Cert-ZC10-15070011/dp/B0151Z8ZQY