The "flashing" ones have armor, use armor-piercing stingray missiles against them. I think by the midgame with lasers and the armor-piercing upgrade that laser cannons are your best shot for everything regardless of armor, since they will upgrade to Pulse Lasers for free once you research them. But weapon stats and what affects them isn't exactly exposed so it's hard to tell.
I'd still argue that getting as many satellites up as possible is always a good idea. Continent bonuses are always powerful, an easy +200-400 credits a month for Africa or North America in addition to getting more from the individual countries. On Classic my limit to satellites was Engineers, which you just have to twiddle your thumbs and wait for the requests to come in.
So long as you start USA you should be able to shoot down the majority of small/medium UFOs for most of the game. Build at least 2 more aircraft in month 1 and get around 4 new aircraft for each new continent you take.
The Transports are a PITA to complete and frankly I don't think it's really worth much even if you win. You simply have no use for the 50-60 or so Elerium and Alloy so early, so you're going to end up selling most of it. But by assaulting the Transport you've set the AI "back" a lot and because of this you now get only 3 meld from canisters for the next month or two when normally you'd get 6-9, and getting around 5 meld more for 20 missions is a LOT of meld even assuming you only get 1 canister per mission. Meld goes for 7 credits each vs. 5 credits for Elerium or Alloy, and Meld is obviously worth far more when needed for essential foundry research or when used for country requests (and I haven't even gotten into MECs for lack of meld yet). But if you do assault them then one essential tip: Outsiders can't climb ladders and will happily cluster below your units and wait around.
is it true that the new Enemy Within enemy faction is annoying as fuck with Long War and swarms you with like 50 dudes at a time
I've heard lots of complaints but I have no idea why people struggle. I actually did the first 5 or so without even knowing about the transmitters and only figured it out when EXALT got laser weapons and I looked online about disabling their weapons. Once you do that the mission is a ridiculous piece of cake. Just know that the guys with Rocket Launchers IIRC have grenades and shit they can still hurt you with, so gun them down first.
As Gozma says, abuse Assaults (frankly the class is useless outside of EXALT anyway). Keep in mind that you can't use Run and Gun if the pistol is empty, and close combat perk causing you to shoot nearby enemies can empty your gun.
Make sure you use the Exalt Scan option at least twice a month to avoid their attacks draining your money or research. Another thing that I didn't even know you could do in Vanilla because EXALT were so easy that there was no need to learn.