Red Phantoms are actually black phantoms in the game taxonomy, but they definitely look very red. The visual style represents either invading players,unique npcs or recurring npcs. The latter two categories are mostly triggered by changes in world tendency although some are scripted in to certain areas iirc.
Unique NPCs would be like the young lady (Mirelda the Executioner) with the guillotine axe, and are generally challenging but can be gamed by sneaky players since they have very strict AI limits. For instance, one is a spellcaster you can trick into wasting all of her magic, after which it’s clobbering time. That’s another great thing about this game, most enemies play by the endurance/magic rules that you do. You’ll see them in the load screen along with helpful NPCs, and most(not Mirelda!) have a good incarnation in white tendency that you can do quests for and an evil one in black that tries to fuck you up. Generally, they have some of the best items in the game.
The mob of other dudes would be the unnamed, generic variety of black phantom, which are marginally harder than a regular enemy (although it can seem daunting at first, especially in groups). Generally they will be very similar to the standard foe they resemble but have more health, stamina, and damage output.
I don’t think you’ve described any of the unnamed, unique NPCs but they are some of the more interesting encounters in the game by my reckoning. There’s one with a meat cleaver you’ll see later on, a real son of a bitch.
If you’re having trouble getting through the dragon in time, it might be that you are overly encumbered. If you drop some armor that will get you to your fastest running/moving speed (where you no longer do the “roll, thump” when you dodge but simply roll) and makes those sprints pretty comfortable.
The massed crossbowmen require you to have some presence of mind amid the adrenaline, and really master the timing around lowering your shield before the next wave of arrows comes at you so your stamina and weaving around can do the rest. I strongly recommend getting the bow that’s on the top of the first tower in that wall run and then getting enough arrows at the vendor (I think around 200) to kill the dragon ASAP, so that you can deal with the bridge-dwellers at your leisure. With the Royal (has the magic regen ring) it’s actually possible to use the bow’s aiming to target your magic missile manually, then plink away at the dragon for free, then wait to regen, and so on.
Anyway, you can find videos for how to kill the dragon off that first towerall over the place, and it’s well worth it imo just because having to do boss sprints through that dragon (if you don’t get him the first time) is irritating. Plus 10k souls will only be valuable to you if you get it early on.