Hi, welcome to the forum!
I'll answer what I can and let the senior members take on the big stuff.
How often do RES turtles Bask? How long?They should bask everyday. Mine like to bask for hours daily. I wouldn't time their basking areas to meet a quota, but let them bask naturally. I believe turtles will bask when they need to. We can't force them to anyway.
"When you get a new comer, how long does it take for them to figure out how to bask and get used to things."
It depends on the turtle's personality some will learn and adapt faster or slower. I'd give it a few weeks and try not too change too much like moving the basking area or decorations unless you have to.
The water temperature is fine, but you might want a heater for winter time.(You might want to upgrade your filter. The recommended filtration for turtles is 3x volume list on the box, the)
For feeding there are many different answers and I cannot say which is right. On this forum we have a discussion of everyone's turtle diet so we can compare.
viewtopic.php?f=8&t=11684I personally feed my turtles pellets once a day while i introduce him to some greens. Many on this forum feed turtles the amount of food that will fit in side the turtles head if it was hollow because it's the same size as their stomachs.
Also the
Feeding and Nutrition section of the forum has suggestions for food
viewforum.php?f=8It takes time for turtles to build trust(We are quite big compared to our tiny turtle friends so to them we're predators). It's quite normal for your turtle to hide in its shell and peek out when you pick them up.
Shedding is normal for turtles.
To entice basking the water and basking area temperature should be about a 10F difference(If the water is too warm or the air is too cool turtles won't bask). Turtles also like their privacy when basking. You can try peeking around a corner to see if they're basking.(Until they get use to you.)
The site says to keep the water 75-79 for adults and 78-80 for hatchlings. 84F is probably too hot for turtles.
72F is okay for now, but you should get that heater.
If you turtle attacks your heater you can get a heater guard or make one from pvc pipe. You could also angle the heater so the cord is out of the water, but below the minimum water line. (Depending on your heater)