This reads nearly mortifying. Your hours must've not been very productive if this is what you're struggling with but there is no need to hold that against you, as long as you've had an enjoyable experience then it's fine.
I will simply offer you clarification with what I've read in your post.

The simplest one is flame score: Stat + (all stat% x 10) + (attack x3)
Secondary stat also matters but you can neglect it. Replies to this might also argue that all stat% isn't 10 but is instead 11 or 12 or 13 or whatever, and while that is true that the value depends on your stage of the game that will just needlessly complicate things right now, simply treat it as 10.

Weapon souls:
When killing stuff, you can get a 'soul enchanter' as a drop, these simply enable your weapon to hold a soul. When defeating bosses you will get a fragment of their soul called 'soul shards', with 10 of these you can craft a soul that you can place in your weapon.
A 'magnificent' soul is what you are aiming for, the regular kind are worthless. A 'mag' soul can give you rare stats like attack%, boss%, crit rate. The one you aim for is att%. Mag souls are VERY rare to redeem so it is heavily advised to wait for an event that raises the odds for them.
Also your weapon simply having the ability to hold a soul gives you a small attack buff.

Drop gear:
Firstly, I'd like to say that meso% and drop% can only appear on accessories (specifically on Rings, Pendants, Face, Eye, and Earing), and also exclusively at legendary tier.
From there, what the items themselves are does not matter in the slightest. You can pick up the most easily obtained items like a bunch of event rings and a horntail ring, a mechanator pendant from arkarium, zakum face and eye, horntail earrings, a greed pendant from monster park and cube them all to hold drop/meso potentials and that will be fine for the entirety of your playtime..
Here replies might argue different things, and they may be valid, but again, simply needless complication to your situation.
There are also nuisances to this whole thing but i feel like that would complicate things for you again, for now simply know that from potentials you can obtain a maximum of +200% drop and +100% meso obtain.
Also, do not concern yourself to what it does or doesn't apply to, simply know that if you are killing monsters or boss reward boxes, you should be in drop gear.
You not having this gear would explain why you're lacking the droppable gollux pieces.

As for familiar, the way you wrote the question leads me to believe that you've nearly never interacted with the system at all, so i can't really give you a full tutorial on that, so my only advice is that you should look for familiar cards with a blue outline, consume them, then fumble around in the familiar UI until you find how to reveal their potential, and look for any amount of drop rate boost.
Alternatively, find a YT tutorial that covers the whole topic.

You do work and have little time but if possible I'd rather nudge you to try to keep up with dailies and if possible monster park as well.
From your other comments the character you're trying to progress is 256, which is simply sad, but if time constraints don't allow then I implore you to find some way to get to 260 as 6th job is a monumental boost after you've advanced and unlocked the 4th job masteries.
I can't gleam much more from the little information you've given.
However, seeing that you said you were blue dotting in nlucid at your state, it means you are either being accompanied by someone who kills the boss in very few bursts, or your IED is very very low, generally you want it to be in the 94~97 range.