Yes, I think the new(?) "Federation Minefield" mission is essentially the old "Punch Through the Federation Blockade"; which back then was basically a mirror to the FED version vs. Gorn (yet was still quite fun as KDF... being the underdogs in badass ships and all). It's now been updated to a strictly 5-man event where everyone rushes the final objective to score the big lewts.
Anyway, the daily still calls it "Punch Through the Federation Blockade". Yay KDF progress!
Well, in my opinion this mission is a Tacscort one (most of the time when I play it is 5/5 tac captains and escorts/raiders etc.).
To be honest I am not fully sure how much everything is worth but the missions are in sets.
Secure Transports and Kill frigates
+Get resources from asteroids
The first stage needs to be completed before the next one beginns and then the same. You want to be fast and kill the enemies quickly here because you will score on the saved transports and also do some of the 20 frig kills, aim for them before the third ship in any formation is what I would recommend.
You want to go from asteroid to asteroid as fast as possible. So using APO, Evasive Manouvers and engine batteries is recommend to get a good score in this part.
Some asteroids have resources available that give a bonus to your score if you get them.
Being the last guy to get the 10th transport is bad, this means you are engaged longer whil the others have mostly gone to the next stage and killed off most of the ships before you can arrive there. This does lead to the transport counter being at 9/10 and all players hanging around in the second stage. Mind you, there is an option to transwarp to it when you are out of combat which takes away a potential long flight time.
The mission says that you have to secure the asteroids (3 times per asteroid). But first you need to kill the respective group guarding it. I am not sure but this might be important to do well. Generelly I would recommend to kill as many ships first and then going for the asteroids.
The one to be last here will usually also be later to the next stage and thus missing out on damage done.
Important is of note that you should have all of your buffs ready for this, debuffs are optional because they will also help the others and not only you (trust me, playing on KDF is bloody competitive in some cases).
You can try to do better by staying at a certain range and cloacking after the message came, run in and get the 15% decloack bonus atop of everything else, also use your tac cooldown ability to have your highest damage BOFF abilities running as much as possible to get a higher place.
Dilithium. I think this is the same ammount for everyone.
Gear: 1st Place Mk XI purple, 2nd Place Mk XI purple, 3rd XI blue 4th/5th XI green.
The gear is random and I have seen a few rants about getting 2-3 purple XI engines and have had the same problem myself. On the other hand getting and XI dmg concosole is very nice if it is not a projectile one because it sells for over a million EC (always check the market first )
Hope this helps, because this will make getting stuff just more difficult for me when others know these things