yes your mother would survive just fine, but i would agree on hydro not being the system for your first mother plant. It's too risky, and gives very few advantages. You're never going to be able to flower under 45 days, and even under fluorescents mothers will grow plenty of clones in that time. Soil for mothers.
Also, are those the llittle red misters in your pictures? They seem to be mounted horizontaly, which is nt what they're designed for. They should be vertical, it will improve their area of coverage substantially. These things are designed to work with gravity to produce a fan of water. Placing them on an sort of angle sharply reduces their efficiency, unless you have a high preassure pump.
You must lightproof the res. I would say you also have to insulate the top lid with some sort of reflective insulation, or else anywater hitting the lid from underneath will be heated substantially by the light hitting the lid from on top. Res temps are the hardest thing to crack in aero, you need it below 72F qand ideally in the mid 60's. I have found gains of up to 15 F after covering the res lid.
No medium will probably work, there are lots of ways to suspend the plants, but i would use hydroton in netpots in aero to give the plants stability. They can fall over REALLY easy otherwise. Your roots will still get big, providig a counter weight to tht eplant in the res, but my plants have gotten HUGE in 30 days, and definetly need the support so they dont get owned when im changing the res and moving them arround.
I use my aero box for vegging and flowering. I would clone in it if i had to, but again i would be sticking cut clones into hydroton and running it to wet the hydroton untill they showed roots. I in fact am going to be using jiffy pellet to hydroton clones in my aero system next because my soil cloning is RETARTEDLY more succesful then my many experiments in hydro clonig. To clone in hydro, build the Stinkbud system listed on this site and ull need a 1 minute on 5 off timer which is almost 90 bucks, but it is the key to good hydro cloning.