A1: Mythology is indeed gone. We cannot obtain it from any vendor in Eorzea. The only way to get it is to do the new expert dungeons[Snowcloak, Stasha HM, Quarn HM]. Replacing Mythology is, you guessed it, Soldiery! Soldiery replaces mythology just like Mythology replaced Philo all those many months ago. I personally don't like it since between 2.38-2.4 I was able to buy myth gear with Allied Seals and then desynth it in a few days with 2.4 and you can't do that now because Mythology was taken out of the Allied Seals vendor.
A2: Alexandrite is still here. You can still get it from doing the expert roulette and buying the Mysterious Maps via soldiery[not sure how much]. You can also buy Alexandrite for 200 Allied Seals[which I will get to in your later question]. Overall I personally think Alexandrite was easier to obtain in 2.3 because of the inflation of Mythology.
A3: The currency known as Allied Seals is the reward we get from killing hunts scattered across Eorzea and completing the daily/weekly mark bill. There are many uses for Allied Seals.
A4: At this point with the weekly lockout gone, CT2 is the best option since you also get 50 soldiery which is very good with the short time, compared to CT1, it takes to complete. Other than CT2 and SCoB you could buy sands for 750 allied seals and oil for 500 allied seals but frankly with CT2 that looks like a complete waste of seals at this point.
A5: I encourage you to get Nexus and be ready for the next upgrade. Right now Nexus is kind of moot when we have access to ilvl 120 tome weapons and ilvl 135 coil weapons, leaving Nexus at ilvl 115. But in time I believe it will measure up to those opposing weapons. Novus and Nexus is not easy and is, in my opinion, so far the hardest stages of the relic weapon. For nexus you must soulgaze your Novus and complete duties to obtain "light[general community calls it light]" progress for your Nexus. In short your Novus must get 2000 light and easy category of duty can give different values of light.
A6: Eh. I personally don't know since I try to stay out of EX DF content. But we must remember there are always new players across many servers and unfortunately gear elvel and echo can only help so much.
A6: Savage Coil is the harder version, if you will, of SCoB. I personally don't know all of the lore behind it but I do believe it is, simply put, the design of the fights that SE could not beat with the set gear level or bare to even give to use when we were not even close to being ready[matter of opinion, though.] The only reward from completing this savage coil is an achievement with a title reward, no loot.
A8:
Desynthesis - So you should know about Desynthesis. Desynthesis is the concept of players desynthesizing items by breaking them down into items that would, in theory, be used to craft the said item. It gets very wishy washy when you look into CUL desynth because you can indeed desynthesize a fish for a pair of sandals. What you NEED to understand is there items out there that can only be obtained via Desynthesis and these items are also used in many crafting recipes so in a way Desynthesis and crafting go hand in hand. In 2.3 the best gil, in my opinion, was in desynthesis.
Ramuh: Ramuh sucks. Hopefully you find a group with some brains and the attention span to focus for 10 minutes at a time. I mean no disrespect, that is just my opinion of the general groups I run into most of the time.
Hope that helped. If you're ever on Lamia give me a call!