Anyone used 105/Tiagra brakes with MicroShift Shifters?

I've got a Forme Rapide which (I think) is the predecessor to your bike and (I think) comes with the same groupset.

I tried a variety of different calipers (SRAM, Campag and Shimano) and had big issues getting any power and modulation. In the end I found that some Tektro R539s did the job absolutely perfectly, and they turned out to be a great upgrade. But yeah, there was a lot of trial and error.

I would try just new brake pads first unless I was going to go for something substantially further upmarket tham Tiagra.

If you're asking if shimano is comp. with MS levers then yes !

It depends on which generation caliper you are using, the newest ones do have a slightly modified cable pull ratio. My experience of Microshift/Shimano 105 (5600 model) goes like this:
Original setup, SRAM levers, 105 (5600) caliper=great feel, power and modulation
New setup, Microshift levers, same calipers and blocks=crap (especially when braking from the hoods)
Result: New SRAM levers, Microshit Centos levers in garage (make me a sensible offer if you want them, black, 10 speed, done about 600 miles).
I dont know how the newer generation Shimano calipers will be with your levers though.