I'm not who you asked, but I've cleared all content on all difficulties, and I'll try to answer your questions.

is there an order to do them in

There are 9 total raids so far. Yes, if you care about learning the story of the Dread Masters in order, otherwise no.

6 are directly related to them in this order: (Karaggas Palace, Explosive Conflict, Terror From Beyond, Scum and Villainy, Dread Fortress, Dread Palace).

There are 2 raids that are stand-alone (Eternity Vault & The Ravagers), and the last one that is directly related to last years expansion Shadow of Revan (Temple of Sacrifice).

easily pug hard-mode raids

My experience has has shown that no they are not easily puggable unless they have cleared the content already. That falls to story mode only, and even then you'll still get players who refuse to learn mechanics, learn their role properly, or even be geared. The bolster you get from using group finder to run story modes make this less important though. However for HM/NiM knowing other people in game who have done progression can help if you need a sub for the night though.

Is there a system to pug NiM/HM raids, and are there weekly lockouts once you kill bosses?

Other than spamming fleet chat or belonging to an actual progression group, no, not really. Story mode there is a group finder, but most of the time people spam chat to form a group first then queue up.

Lockouts yes, there are separate ones for every boss on all difficulties.

DPS meters and such

Yes, there are a few different tools out there now that make use of the combat log. The most popular ones are Star Parse and Parsec. To make use of the group function though, everyone has to join a group created using whichever parse tool the group is using. Story mode pugs generally don't use them, but for actual progression groups they are a must to see how everyone's doing.