There are a few roads where an RV over 8 feet wide or over so many (varies) feet long is not allowed. However those roads are few and far between. On most roads the max width for RV's and Flat Bed Tow Trucks is 8 1/2 foot (By the way, I've driven both, though I only drove a tow truck one time. (I'm not licensed for tow trucks, it was an emergency and empty and I was not paid to do it so I sneak in under a loophole but I'm not licensed to drive them)
Somewhere there is a list of the roads you can not travel but any freeway is ok, the prohibited roads are mostly residential or "Old town" Business, (narrow, sharp turns, that kind of thing) The length restrictions are on roads with very sharp turns a long rig can't make the turn
Statutory heights in most states is 13' 6" for truck routes. It is more in others. Your rig seems quite high for most RVs. You might want to measure if you haven't done so already. Usually they are under 13' but I'm not familiar with all the models out there. If you really are 13' 4" you will have to be very careful even on the Interstates! Most Interstates seem to have even more clearance than the statutory requirement.
If you pick up a copy of the Rand McNally Motor Carriers' Road Atlas you will find charts for low clearance, width restrictions and other information. Really handy to have at times.
Yes. As Jim says, most eastern states set 13'6" as the standard underpass height, but there are a number of exceptions for older underpasses that existed before the 13'6" requirement and places where it simply wasn't feasible. They will be marked. Also some gas stations and such with covered drive-thrus may be under your height - 12'6" is not unusual. In other words, you will have to keep your eyes open overhead.
Newer highways will have higher clearances, typically 15 feet or more wherever feasible. Western states generally follow the newer standards because the road systems were designed and built later than eastern regions, which have roads dating back to colonial times.
You will also have to be extra cautious of low hanging tree limbs, utility wires and such in & near campgrounds.Everybody has to, but at 13'4" you will be more at risk that most.
We had a high profile(13'2") fiver for two years and had to make a few detours on highways and were invariably scraping tree branches in wooded campgrounds. Not a traveling disaster, but definitely requiring the driver to be observant at all times.
I30 in Greenville TX - if I remember right is only 13'4" - eastbound. They have overheight detection thingies all over the place and if they light up, you take the off-ramp, go thru the intersection, and back on the on-ramp. My trailer is 12'6" to the top of the A/C, and the first time I went that way, I even cruched down in the seat waiting to hear the dreaded sound of tearing metal even though I knew I had 10" to spare. I still catch myself ducking my head - just like it would do any good, everytime we pass thru that area.