What are advantages and disadvantages of flaperons?
The main downside of flaperons is you can't lower them as much as a regular flap because it has to still do its aileron function when "flaps down".  This means the downgoing flaperon has to be limited to its "lift generation" range when the flaperon mixer is moving it to full down flap plus full down aileron, and can't exploit the "drag generation" range of a normal flap because the resulting adverse yaw is extreme and the roll rate drops.  

At the same time, the inboard end of the flaperon contributes marginally to roll control, the roll arm being short.  And you are also limited to the use of differential aileron gearing as an adverse yaw reducer due to the need to keep the flap function reasonably symmetrical.   

You end up with a flap with limited extension and therefore limited utility as a flap, and an aileron who's inboard end doesn't do much for roll control.  These issues limit their potential effectiveness to being marginally better than a well sized regular flap and aileron. 

The principal advantage is you can get a lower overall stall speed because the early high lift range of flap travel is available across the entire span, and you have a much simplified control system since you are combining aileron and flap on one linkage, with some form of mechanical mixing device in the fuselage.

So, like so many things in aviation, they may seem like an ideal solution and have their place, but the limitations and disadvantages are significant enough that a majority of designers prefer to go with the separate flap/aileron.