1. I have read various times that repeated super charges are bad for the battery. True?
2. I am planning on driving my Model 3 AWD round trip from Columbus Oh, to Seattle Wa. 1.4K miles each way. Will that damage the batteries?
3. Is there any way to mitigate that?
The folks who've had issues here are ones who supercharge daily (or weekly) for years- not who take the occasional road trip.
Even then it's more like slightly accelerated degradation over hundreds of thousands of miles, not over 3000 miles.
Ideally you will want to do a little planning about which SCs you intend to stop at each way- and there's pretty much 2 ways to do it depending on your plans/goals.
Option 1- Most efficient time-wise is: stop when you're down to 10-20% charge- charge just enough to add enough range to get to the next supercharger with 10-20% range (usually this'll be like 10-15 minutes but can vary depending where you are, the charge rate you get, etc)
That means stopping more often, but for usually a lot less total time than full/near full charges, because the charging gets slower in the top half, and MUCH slower in the top 10-20% of charging.... and gives you more chances to take a few minutes to grab drinks/snacks, use restrooms, etc...
Option 2 is if you plan to stop for sit-down meals instead of eating in the car you can build those around charger stops and let it go to a much higher charge (even over 90% is fine since it's not going to "stay" that way for long...). This probably means more total time charging, but you're planning your meals around that so it's not "wasted" time.
Other thing is, either way, if you plan to use hotels along the way- try and find ones that offer an L2 charger in the parking lot so you can charge more slowly overnight and leave with a full charge rather than having to worry about fitting another SC stop in relative to hotel stays.... they're getting fairly common now so shouldn't be too hard to find.