1) The entire visit may not be,
but a large portion of the tests should be, unless your plan is grandfathered in, which seems unlikely if you just switched.
3) You don't have to; if your total medical expenses (including dental) are over 10% of your AGI, you can deduct all of them (minus any that you used HSA for, if you have one). If the premiums alone don't push you over that threshold, you probably shouldn't have the HSA (so you can use those costs to push you over), but if they do, it may make sense to have one for convenience and to simplify bookkeeping, and to bank pre-tax money for the future.
4) Re OOP, I just wanted to note that for most pre-ACA plans, the OOP maximum wasn't a hard maximum, it was the point at which the higher level of coverage kicked in. Under the ACA, it is actually a maximum.