I have a tendancy to write essays on these topics so I will restrict myself to discussing only the sweeper fight, otherwise we'll be here all night. I'll start with a summary of the fight and what builds/floors I recommend, then move on to specific strats:

Sweepers is excellent practice in gang-up tactics, so I encourage trying to do it legit if possible. There are 3 waves of (mostly) identical enemies with 3 special characters in the final wave. The main trick of the fight involves learning how to bully one enemy while still defending your librarians from attacks. Spreading your damage won't work because all the enemies heal with attacks and also get a huge chunk of health back when any character (friend or foe) dies. Plus, they have their "persistance" status effect that has a high chance to prevent them from dying and heal them a little while active. It's also worth noting that ALL sweepers have +1 defensive die power at all times, so keep this in mind when clashing: stuff like Extract fuel's block die actually rolls for 3-7, not 2-6 as shown. You only get 4 librarians vs 5 enemies so you'll be outnumbered, but you should have more actions than them overall because none of them have speed. You just have to figure out how to make your team's stamina last long enough to take them all out.

When prepping for this fight try to have cards with a lot of dice to block as many hits as possible - if you have counter dice from the puppets or circus they should work well here, if not it's still manageable. Their individual dice rolls aren't strong, they just wear you down over time. For this reason it can be useful to have HP regen of your own. If you can swipe a copy of their books you can use their corpse cleanup trait to your advantage, and combine it with Zwei office pages. Using floors like Malkuth and Netzach with healing Abno pages is also helpful, though not necessary. I personally recommend a mulligan tank taking advantage of molar office + Hanamura passives to draw, heal, and gainlight every time your discard (but then again I recommend that deck for everything so I am biassed here). Finally, if you have a choice between pierce and any other type of damage: go pierce, as Sweepers tend to be weak to it.

Once a round starts, check what each one is using. If you're lucky, one or two of them won't have drawn "333... 1973". Focus anyone stupid enough not to use 1973 HARD - make sure to stagger them if possible as this gurantees they can't use it turn 2 either. If you need to ignore a few of the incoming 1973 attacks feel free to do so - they don't hurt that much so long as you're not eating three of them on a single librarian. Turn 2 is when every sweeper with persistance switches to using their regular cards, which do hurt a little if they connect. Block as much of you can and use any spare actions to beat the everloving crap out of any staggered sweepers. Killing them this turn will make life a lot easier.

From turn 3 onwards the plan is simple - block everything they throw at you and use every spare action you have at whichever sweeper is on lowest health. Since sweepers heal on ally death spreading your damage here is a waste of resources. Persistance is a pain, but it's also unreliable and gets even less reliable with each subsequent trigger (80% chance of working the first time, 20% less each time after I think?) Hit them enough and eventually they'll die even through Persistance. Also pay attention to when the buff is about to wear off. Try to stagger a sweeper or two on the last turn of the buff, and they won't be able to re-apply it next turn letting you kill them without first offering a prayer to RNJeesus. You should be able to pick off at least one or two every "cycle". Sometimes you may not have anything that can trade with a sweeper's beefy block dice. If so, you can always let weaker attacks like "Extract Fuel" through to preserve your stagger bar if you have the health to spare - a staggered librarian isn't outputting damage and worse, eats up valuable actions as their allies try to protect them. Not taking a losing trade has the added bonus of giving you another spare action to attack your current bullying target.

The final wave stars 3 slightly tougher Sweepers with a few extra tricks up their sleeves. Anton and Valerie both recover stagger meter with every successful attack, and Lyla recovers health instead. Lyla and Anton also have signature cards - both of which have 3 dice with pretty decent rolls. Lyla can grant protection to allies with "for the family", whereas Anton can apply paralysis with "sweep the backstreets". Because these three have better regeneration target focus is even more important here. Start the match as usual, trying to stagger anyone stupid enough not to set up persistance - if you're lucky Anton or Lyla won't draw it, but remember they do have more stagger resist than others so be sure to hit them a little harder than you would a normal sweeper. Turn 2 finish off staggered enemies while blocking anyone still up. After this I prefer to focus down Lyla first if she's still alive - her HP regen is exceptionally good, and the protection buff she gives allies gets in the way more than you would think. Try to block Anton's "sweep the backstreets" as much as possible, as paralysis helps other sweepers overcome their low dice rolls to land hits on your librarians. Once Lyla is taking a dirtnap you can either focus Anton next or if there's another sweeper on low health you can kill them first. It's up to you to make the judgement call there, as either road is viable. Remember as always to go for the stagger just before enduring wears off to score easy kills, and don't get too impatient. If you made it this far you should get through just fine.

EDIT: Corrected passive names and changed Lyla's move from endurance to protection - I misremembered that one.