If you never played DeI, you should have not started with Hard difficulty.

Economy and Public order are very easy to handle and even if your example, game exactly told you what caused your public order, you just hoarded slaves (you can sell them with sell slaves edict), some events happened and buildings you built applied a lot of Public order penatlies but when you pick buildings, their description tells you their effects.

Diplomacy is also very easy if you work on it from start. One of the common issues people raise is that Trade Agrements are too easy to get and they were even asking us to try and make it harder or hard cap it somehow (which we wont). To understand TW diplomacy, you need to know 2 key factors, RNG, each turn EVERY faction you know has % chance to randomly declare war, CA added this to not have a situation where everyone likes you and nobody declares war on your first. Another is snowball effect of diplomacy, every action vs X faction will also give you diplomactic change with Y faction. In terms of wars, the more wars faction has, the more likely AI is to declare another war against it, as in AI eyes, that faction is easy to beat due to sheer amount of enemies. To make diplomacy work best, invest in it from start and always keep very minimal diplomatic partnes, like maybe 1-2 NAPs/Alliances.

Difficulty comes to play here too but so far I never had a civil war in DeI, despite being medicore player at best. There are some events/decisions on player part that can make it worse but if not neglected, you can navigate it and never face any revolts.

The thing you need to realize is that there are very wide and deep number of options for you to navigate through. Since you only recently started playing the mod, you know very little of these options. Diplomacy as mentioned by kam a central mechanic that, if neglegted, will make you the pariah of the world that has no friends and which everyone wants to take a bite of. Additionally utilizing all of your characters to their full potential and in synergy with your plan for everything else that you can do, for example what buildings to build in what regions and provinces and many other things, is totally key to navigating successful through the maze of options that will lead you to success and avoid all of those negative consequences that you mentioned.

Play on Normal as Rome, and it should be quite easy actually. Just remember to focus on diplomacy from the beginning. Carthage is rigged to hate you, as is Epeiros, so peace will be nigh impossible. But given that Epeiros and Carthage are the initial main antagonists when playing as Rome, you should secure friendships with the factions that are against them, turn neutral factions against them, and befriend/ally with factions that can threaten from fronts on the opposite side of your empire borders. You don't want to fight a horde invasions from angry central/south/east european factions while also having to deal with numerous invasions from the war against the mighty Carthaginian empire.

And keep in mind that Romes units are super strong and not so expensive. Principes and triarri as heavy infantry and good cavalry, all having a ton of armor, will totally destroy everything. But of course not automatically, you still have to use them tactically sound. And city of Roma can spit out godly numbers of these units every turn, so raising armies is done very quickly.

Final note; on loyalty: Factions get permanently more loyal to you when their characters get promoted. So using them for generals that will then result in their possible promotion is a very good idea. Make sure to get them married and send their wifes on mission, as wifes gets autopromoted whenever they go on a mission (males will not) and for each wife promotion level comes more loyalty. Hire more characters for factions and marry them too. Very loyal faction generals will give the units in their army a nice -9% unit upkeep reduction, which can combine with significant upkeep cost reductions from general upgrade cards, promotions, government type, from agent accompanying the army AND from research. I believe you can probably end up getting close to -50% upkeep costs, which is obviously extremely significant. Especially useful for super elite armies with very strong and expensive units as the savings will be that much greater.