It is no longer possible to sail Privateers into foreign cities, even if they're your vassal's.
As to Combat1 vs Drill1: for otherwise equal ships, if the defender is on Coast and has Drill instead of Combat, it has a slight edge. The Coast is essentially worth 1 Combat promotion, and so if you have Drill, your free shot gives you the odds. When reversed, though, a defending Combat ship will defeat a Drill ship most of the time.
Giving Drill promos to Privateers tends to be useful, until they encounter Frigates. At that point, the Privateer needs 3 extra Combat promos + being Coastal to have a decent shot. At that point, you need to pair up your Privateers and start moving out of the area. The enemy will start pairing up their Frigates too, so you may as well move on to someone weaker, or withdraw to your own harbors and await the occasional passerby.
Privateers tend to have a short lifespan, but their free Sentry promo makes them worth building for when you later upgrade to Destroyer.
Stealth Destroyers can no longer bombard, and they don't defend against anything but other Stealths, but they can still pillage without being seen, and they can also smash enemy transports that the enemy thought were safe behind friendly lines. Just don't start blowing up fishing boats and give away that you've got them in the area. They also make good tattle-tales: Park one with Sentry near a couple enemy cities and it's as good as having espionage. Park a little further back if you have sufficient espionage, particularly at a choke point, and you can watch the enemy navy come and go.
Building Red Cross on the coast also allows you to build ships with Medic 1 for free. Often, I pair Red Cross with West Point, then build Pentagon somewhere, and with Drydock and a Military Academy, I get 3 promos AND Medic 1.
My typical promo prefs:
I usually give wooden units Combat, to give them whatever edge I can, since they're not too likely to get much in the way of promos. Galleons usually get built with Drydocks, so it's possible to make them fast out of the gate.
For Transports, I always turbocharge them. Rapid transport is their only mission, so speed is the priority. Having them also be Hospital Ships to heal the Marines en route to the next conquest is handy, and saves me needing to waste a promo on another ship that wouldn't likely be sailing with it anyway.
If you have the tech lead, initial Destroyers should also be turbo-charged, to get them in and out of trouble quickly. Build a few up-gunned ships to head toward Blitz, to clean out the masses of enemy wood floating all over the place.
Battleships DO fall easily to Destroyers, so gun them up! Occasionally you can throw in a Barrage boat, but most should go Combat.
I like turbo-charging Carriers for the same reason as Transports, and if they have that free Medic 1, then planes heal, as does the necessary Carrier escort. (I send Transports all over the place without a second thought before enemy Destroyers appear, but I wouldn't think of it for Carriers unles I'm at peace. Just a quirk.)
Subs, I like to give them Flanking. They're slow and weak. If you want early missile support, give them Turbo and keep them with the Carrier (that is, keep them protected). This way, the Battleships are what's slowing you down, and Battleships aren't all that slow, and I like all those big guns. And Battleships can upgrade to Cruisers, which are faster.
I like keeping an Attack Sub or two with my CVBG, in case I need some sort of naval cavalry (high retreat odds). I may have some as messengers, and those get turbo-charged. And I keep a few sitting around my coasts to keep the DDs company.
A Cruiser is just a Battleship with missile-carrying ability, and is a little faster. Some people say it's not worth the money to upgrade, since you gain little, but the extra speed means that your Carrier is now the unit holding up the CVBG, but since it's already turbocharged, there's nothing to be done. At least now the Cruiser can bombard defenses without holding up the group further.