Bad news first:
People in the Uni apparently still don't know how to fly Caracals
I've seen a number of AARs in the past few weeks where an FC used Caracals badly, welped, and then decided to stop using Caracals "for now". This is a common error new FCs commit (use an unfamiliar doctrine, screw up, blame the doctrine, design a new doctrine that is almost always worse) and the only cure is
I've written some advice on how to use each of the BLAP doctrines (and I think White 0rchid has written some for Caracals); I think it's still on Titus' sandbox wiki page pending full publication. The short version is that Caracals must take advantage of their best-in-class mobility (as a fleet doctrine, Caracals are the fastest T1 cruiser) to control the terms of any engagement or else you're just feeding. This also involves recognizing fleets that outclass you in mobility, typically because they aren't T1 cruisers, and avoiding those engagements.
Know your enemy. Spend some time on zkill and talking to more experienced FCs about common doctrines and what different sorts of ships do.
In this AAR, you blame indecision for the two major losses during the fleet (to HCOOK and WAVE respectively), but this indecision seems to be a product of insufficient knowledge - you did a good job running the Geddon fight because you thought you understood what was going on, but it doesn't seem to me you fully knew what was going on in that fight either. Not knowing stuff is okay - fixing that is the Uni's purpose - but not knowing that you don't know (or not admitting to it and asking for help) is not okay. (If you're asking for help in the FCC, I apologize - in that case, you're doing right, but should more explicitly admit your screw-up in the AAR.)
Omens come in two flavors in fleets: beam fits (which should usually have ABs) and pulse fits (which should usually have MWDs). I don't know what they used in your engagement, but Zkill shows that HCOOK lost a bunch of Omens to Moas a few days ago and the fit was a somewhat unorthodox pulse fit. Your scouts should be using the "look at" feature and looking at enemy fleets' guns to give you this intel. Against pulse Omens, you should fight at range (i.e. around 30km where they can barely project Scorch damage at all, out to 40km where they can only do drone damage), but they're almost as fast as you. As a result, you need to have set up in advance to fight, either by pulling range on the gate and letting them jump through, or by cross-jumping them and pulling range while they crash. With correct FCing, this engagement should slightly favor the Caracals, which is why Captain, above, was surprised that you ran away.
Deimoi also can be flown in two ways, although I usually expect gangs to be using rails as these guys were. Either way, they fly very quickly with MWDs (as fast or faster than you, depending on links and bling), have around 50k ehp, and either do nearly 300 Spike DPS out to 75km plus 130 drone DPS out to 55km or so (rails) or 600-780 DPS depending on blaster ammo at brawl range. Plus they apparently had some rail Hecates. You would be very unwise to fight more than 1-2 Deimoi, without any additional hostile support, with 10 Caracals - and if they are self repped I would expect that fight to stalemate. (Did this gang have logi? None appears on the BR but the logi would've been 100km off and unable to use whore drones.)
Armageddons rely very heavily on neuting, especially in small-gang environments. Your logi, however, are cap chainers, which means they should be able to hard counter the neuting by repping/feeding cap to your tackle when the Geddon tries to neut out tackle. It's possible that your tackle pilots didn't know to broadcast for cap; also, since your logi all died, it appears that the logi anchor failed to position logi well or didn't correctly maintain the cap chain. Again, the cap chain should always hard counter a lone neuter like this Geddon.
"Heavy tackle" still is not really a thing. In particular, Jaguars, and these days even Svipuls, are quite bad for this "role". There are better options and you should use those instead.
For your "heavy tackle" to be effective, you probably need both a scram and a web. (You should really be using a Hyena for the webs, more on that in a minute.) The Keres should be able to hold point on anything that doesn't MJD, so the only things that can get away from your fleet either burn out with MWD/MJD (which gets stopped via scrams) or are 100mn fit (which gets stopped via webs).
The problem is that neither the Jaguar nor the Svipul have enough mids to fit a scram, a web, and an effective shield tank. On top of this, the Jaguar doesn't actually have a very good resist profile without an invul - if you plug your exp/kin resists via rigs, you end up with under 12k EHP. That's pretty thin and therefore not really appropriate for a cruiser fleet. As for the Svipul, you can get better resists from defense mode once you've landed tackle, and you can be a combat prober so you're still a helpful first tackle, but 17.5k EHP is still a bit thin for a cruiser fleet. The Jackdaw is the best of the lot at 21.3k EHP, but still...
The fundamental problem with "heavy tackle" is that it sits in scram/web range of the bad guys, and the whole point of Caracal fleets is to not be at that range. As a result, you're committing 60-70m ISK ships (for the T3Ds - and the Jaguar is just suicide) in a way that either makes them very likely to die or risks your entire fleet. This problem should be entirely clear if you glance at Calaheim's Jackdaw killmail. He took a total of 5,185 "real" HP in damage in a ship that has just under 5k real HP. This means he didn't really catch any reps at all, against ships shooting squarely into his highest resists - probably because your logi were in deep falloff, if I had to take a guess.
Use ceptors for scram passes, ceptors and your Keres to hold point, and for the love of sweet baby Jesus get a Hyena. As soon as you can sit in a Hyena, you have a 40km t2 web before heat or links, and it has almost as much tank as that crappy Jaguar did. AT 40KM+ AWAY. And if you have someone who can fly a Jaguar, they should be able to fly a Hyena too (it's a 2x targeting skill and level 1 in Electronic Attack Ships).
Good news:
Yes, there is some!
You undocked with a pretty decent comp.
A number of fleets lately have undocked with clearly inadequate logi amounts, too many non-doctrine ships or throwaway frigates, etc. The fact that you came out ISK positive in the first engagement is largely due to this.
Target calling was good in the first engagement.
Had your logi survived better and repped/capped up your tackle, you could likely have killed the Geddon. Definitely the right choice to take away their burst damage and support first. Overall well done here; in the future clear communication with your logi FC (which some far more experienced FCs screw up) will serve you better.
Your AAR was excellent.
Very well done here. The fact that I could reconstruct (from your AAR and the BRs) what happened and what was going wrong, not having been on the fleet or talked to anyone, shows that you did the work necessary to lay out your perspective and get the learning process going. Not all FCs do this well - at times, I've done it very badly - and your honesty and self-criticism deserve a lot of credit. They'll take you far.