You are in a loose game, holding A6s on the button. 4 people limp in front, you call, SB completes, BB checks. Flop comes 10/6/2 rainbow. Both blinds check and utg bets, the 3 limpers call, now you.......raise?

Your raise doesn't accomplish anything. If you were right next to UTG, then you could make the field face two bets cold - here you cannot. So call.

Let's assume you can see UTG's hand, it is J/10

That's a terrible assumption to make! No reason to make this assumption. And as I mentioned, your raise does not accomplish anything in this situation. If you were something like MP and could face the majority of the field with facing two bets, then yes, raise. You want to knock out people with your vulnerable hand. You're not folding since you've been given 11:1 odds and you only need 8:1 on your 5-outter.

If the flop gave you 4-to-a-flush, then raising would be fine here since it's for value.

Again you A6s, this time in the BB, a loose mp player calls and a TA player now raises on the button. The author says to call, but I would just fold this b/c the pot is small and the small ace is questionable.

I agree with you. I would fold this as well.

the flop is comes 8/6/3 rainbow. IF I had called before the flop, I would probably just check/fold this. The author says to check-raise here and if the original TA raiser was in MP and the loose player was now on the button, to bet out instead. Do you all agree with these suggestions and if so, do you actually make these plays?

Post-flop, I completely agree with the author. You want to protect your vulnerable hand by abusing the PFR position. You want him to raise it and face the limper with calling two bets cold so you can have the hand heads-up.