1. What timed events are you referring to? The only things I can think of that have time pressure are demon generals <100 days, Belphegor <80 days to save merchant and arguably clearing the festival of greed early to get reading proficiency before Aura starts to suffer reading debuffs.
2. I think a lot of characters are meant to be annoying to some degree. Is this is a good thing or a bad thing? I don't know, but the characters are all on such extremes overall that I believe the message within the characters is that there's a bit of truth to both sides. Obviously Alicia and Richard are much worse, but there's a balance for Aura to find. A lot of the library club are outright dismissive to anything they consider less-than, but the same goes for the cheerleaders. Richard is awful but starts to become a more interesting read around the festival, and then again once he starts entering real-world events more. It's funny and ironic that the brainwashing on Aura is actually having a negative effect on his interests.
3. I've made a few posts on the RNGness of the game before, I think it's pretty heavy on it to be optimal, but 'to make any progress on [nightmare] (I think you're on an old update) feels excessive. Progress is still pretty consistent if you spend time preparing for fights first, however as someone who almost exclusively plays on hardest difficulties, know that this is the type of game where [nightmare] very much feels like a ng+ mode. Play a corrupted run on normal/hard first, unlock all the scenes in the clear room and all the skills (probably barring the 2 at the bottom from the nephlune church since drugs are very strong on a corrupted run) and then go in to hard in ng+. Do a pure run, get as many ng+ points as possible before taking on nightmare. Avoiding non-human/oid enemies is very much intended though, that's part of the fun is sneaking around them and preserving resources. The game teaches you this on day 2 with the spider-queen. The party mentions going straight for the boss!
4. Regarding heals, if it wasn't for that you'd often have no incentive to end the day. Some days are big days, some are small days, where you use your health bar, get low on health, then end the day learning something or upgrading. Save your items for big days where you've used oils to get the most out of your resources. Again, part of the fun imo. Turn order and enemy targeting I'll massively agree on though. Made a post about turn order the other day, and 90% of the time enemies feel like they target whoever they'll one shot. Things like, I didn't guard with Charlotte so the enemies one shots her, or I didn't guard with Paul and John so the enemy uses Cupiditas and one shots them.
5. Weak companions. Intended. Try to not be fussed about them falling in battle, it's hard, but it's kind of part of the lore with Aura as the hero, and the characters themselves will eventually acknowledge they aren't equipped to fully support Aura. That said, allies become MUCH strong post-festival because Aura learns a new ability that empowers allies, which is one of the reasons they don't grow as fast. Also don't underestimate the slime skill. The slime is an incredibly powerful ally after a few good feeds, post-festival and post-bonding, especially once it learns fire morph or wind morph. (Lightning morph is bait, don't waste your time or resources on it.) Fire morph is fantastic for bosses, wind morph is necessary for underwater regions and storm with high magic is an absolute powerhouse aoe auto spell for regular encounters. It gains exp of about5% of the items value, so use expensive items like Ancient Woods on your slime.
6. I don't think willpower becomes difficult to manage until you're sitting at over 30-40 corruption, have true love's ring, and maybe even 'desire to be dominated by evil'. All of those together become problematic, almost requiring emerald teas to be functional on any given day, but if you get to Verdeaux and acquire 30 lewd knowledge (always make this your focus for higher magic attack and what I'm about to say) there's a book that means the first sex action doesn't end the day, which means you can reset your willpower on Hermann for example, get fulfilment+ 3 for example, and be better for it. +30% stats on any day you bang Hermann is great.
7. I agree about some of the bosses, I've never fought the demon generals on [nightmare], but as long as you make it to them before 80/100 days, just pop bloodshot eyes+ for triple stats for 15 turns on both you and your slime and watch them weep. Blessed flash bomb+s blinding them for 15 turns as well.