Ripples are water waves. What do you think?

The rate at the the waves oscillate up and down depends on the cause of the oscillations or vibrations.
For water waves in the open sea, this could be the wind pushing on the water, as well as the change in tide. These factors could affect the frequency of waves.
For water waves in a ripple tank, the frequency of the motor vibrations would determine the frequency of the waves (or ripples) generated.
Hence, the frequency of the incident waves and refracted waves is not affected by depth, hence it is the same for both.

Certainly. This is shown by the animation at http://www.acs.psu.edu/drussell/demos/waves/wavemotion.html
For simple analysis, we assume water waves to be perfect transverse waves.

Mechanical waves need a medium to travel through, and cannot be transmitted through a vacuum, e.g. waves on ropes, springs, water, sound.
Electromagnetic waves are transmitted via changing electric and magnetic fields, and can travel through a vacuum.
Reference: http://www.physicsclassroom.com/class/waves/Lesson-1/Categories-of-Waves

This is an interesting question. My guess is that the initial vibrations around the dipper could be longitudinal, but further away, the effect of gravity sets in with weight of water particles, and vibrations become transverse. No research evidence yet.
May like to read a very old book (1959) on such experiments, also with audio readout!
https://archive.org/stream/RippleTankStudiesOfWaveMotion/Llowarch-RippleTankStudiesOfWaveMotion#page/n0/mode/2up

Q15: Answer should be A not C. Which paper is this question from?

Q16: v = f x wavelength, f = v/wavelength, f is inversely proportional to wavelength.
For the same speed v, as wavelength increases, f decreases, the graph f vs wavelength is a curve as in B.