Difficult Cases for 3MaxSAT and 3SAT Approximation Algorithm
The reason that 3SAT is hardest empirically when the clause-to-literal ratio is 4.2 is because this is the satisfiability threshold (the threshold at which a random 3SAT becomes unsatisfiable with high probability). However, this is a very different type of hardness than NP-hardness. First of all, the model is different: you are generating a random 3SAT instance with a given clause-to-literal ratio, and hardness applies only on average. Second, there is no formal connection between the satisfiability threshold and computational hardness. There are some properties of the solution space which we think make the problem hard near the satisfiability threshold, but this is just a heuristic.

Now for your actual questions:


While there are definitely no formal results, it might be the case that known practical approximation algorithms for MAX-3SAT perform poorly near the satisfiability threshold.
No idea.
You are asking two questions. Regarding your first question, if you had an algorithm which approximated MAX-3SAT only on satisfiable instances, say achieving 99% performance, you could run it on any given instance, and so determine whether it is satisfiable or less than 99% satisfiable. We know that this is unlikely as long as the performance is larger than 7/8. Regarding your second question, the instances coming out of the hardness proof are not arbitrary, so there is a class of formally "hard instances", but I don't think it has anything to do with the satisfiability threshold.