1. Get a cheatsheet into each player's hands.
You know that godsend player, the one who always has the notecards? Key thing there: the notecards.
You've spoken to the group, and they got upset, but you know they cared enough to get the books in the first place. It's entirely possible that they do just forget, or maybe they're having a difficult time with the rules and don't know how to articulate it. Even if they read cover to cover (and maybe they already have), there's a lot of information to parse and remember, especially for new players. Even veterans forget rules sometimes! Still, fumbling through the book for basic rules is not time-effective. My solution is to create a cheatsheet. This has helped me as both GM and player.
Figure out your most commonly used rules. Type up these rules and print a copy for each player. Try to condense them as much as you can. Strip them to their bare bones so players can find the information they need at a glance. Also, since you'll be distributing the same page to everyone, concentrate on rules that everyone uses. I'll discuss character-specific rules later on.
It's just more practical for you to make the cheatsheet. If they don't have the rules down yet, they probably don't know which ones are the most important. You likely have a better grasp, and you're also the one who wants more efficiency. The best way to ensure that this happens is to do it yourself, and then the whole group will be on the same page.
For character-specific rules, though, it's best if the players do it. This spreads the effort around. Plus, you can use this as an opportunity to help re-familiarize your players with their mechanics. Sit down with them and help them make index cards or type notes from the book. Point out nifty features and answer any questions.
Assure them that it will make their lives way easier, because it will. They probably don't like book-fumbling either. They'll also be more likely to use their character's features if they're always right in front of them in an easily-digestible format. It's hard to achieve your full potential if you don't know where to find it. The key thing is to emphasize how useful it will be for them (in character and out) if they do this, not how much worse things will be if they don't. Make it about them and their potential fun, not your frustration, to avoid further souring.
It's awesome that the Battlemaster Fighter took the initiative, though. If this is something he enjoys doing, you could enlist his help! I'm this player in my own groups, even when I'm not GMing. I love having a cheat sheet, so if I'm making one anyway, why not share? At the least, use his notes as an example (if he's okay with it).
2. Make use of existing resources.
Cheatsheets you make will be the best-tailored to your needs. That doesn't mean you shouldn't use ready-made tools on top of that. People often share their own tools if they think they're especially useful. If you need something specific, search the web to see if it already exists. There's no guarantee that what you find will be useful -- again, you know your own needs best -- but it never hurts to try. If you hit gold, that's time and effort saved.
For instance, here are some form-fillable initiative cards that provide a quick reference of initiative order and PC skills, traits, and actions; here is a larger, longer version of a similar concept. Here's a site that generates spell cards. ENworld has many sheets available. It only took me a few minutes to locate them by searching "5e spell cards," "5e initiative cards," and "5e character sheets," respectively. You'll be more successful if you already know what you need, but you can still try searches like "5e game resources" and "5e player print outs" if you're looking for tools in general.
My suggestions, coming from the other side of the fence where I (and some of the other players) feel that the DM plays a little too fast and loose with the rules, and makes changes to things that we think ought to be "canon" for the well-known world we are playing in:
1) Be willing to consider that the player may be right. Allow him to make a brief argument referencing the rules. Then make a ruling. Make a mental note of how often you rule against the player versus how often you change your mind and agree with him, and try (later, outside the session) to assess whether you're being particularly harsh and/or truly weakening one character's abilities relative to the others'.
2) Be firm if you still disagree with him. If he still disagrees with your ruling, tell him, "I need to ask you to go with the DM ruling for the moment and we can discuss it more later outside of game time, to figure out how we'll play this type of situation in the future."
2a) Try to offer the player another way to reach his objective. Say something like, "Look, the rules say that you give away your position if you attack from hiding. If you then, in full view of the enemy, duck behind the same tree, they are going to know where you are, even if you are so well hidden that they can't perceive you. Thus you do not get the advantages of being hidden in that case. Now if on your next turn you stealthily move to the next tree and hide there without being noticed, and then attack, that would be unexpected and give advantage."
3) Ask players not to use the Monster Manual at the table, and to avoid using metagame knowledge about monsters. That said, try not to mess with well-known monsters in a canonical setting without a really good story justification. If you're playing in a canonical setting, Mummies are going to be something that most adventurers will know the legends of, and the way that Mummies are described in this universe really does preclude a "good-aligned Mummy". If there's going to be a good-aligned Mummy, there should be a good story to go with that, to say how that happened contrary to the usual Mummy creation process, that the PCs have at least been given hints about. Otherwise, yeah, it's pretty appropriate for a PC to automatically kill any Mummy he comes across on sight. They will know the stories....
Note that the 5e MM does say (page 7 if need a reference for your rules lawyer):
The alignment specified in a monster's stat block is the default. Feel free to depart from it and change a monster's alignment to suit the needs of your campaign. If you want a good-aligned green dragon or an evil storm giant, there's nothing stopping you".
However, unless there is a good story behind the anomalous alignment, and your PCs have access to clues about that story, I think it would usually be better (and annoy your players less) if you either make up a new monster that isn't in the MM, or be clear that you are playing in a non-canonical setting and using monsters that don't match the descriptions in the MM. Even in a canonical setting, you can play variations on less-legendary monsters, but be clear (out of character) with your players that this is what you are doing. In all cases, allow the players relevant checks to recall some in-game, in-setting lore about the monster you are actually playing.
For example instead of just putting in a good-aligned Mummy you could say, "You see a medium-sized humanoid, wrapped in bandages. Make a religion check". Tell everyone with a low score that they think it's a Mummy. Tell whoever got the highest check, "Because of [some detail that they can perceive] you think this might not be a true Mummy but rather a Pseudo-Mummy. Pseudo-Mummies are created by a different process than True Mummies and in some cases can maintain their pre-death alignment." If you want, you can go into the process more, or you can just say that the character doesn't know any more than that. Now you have a good-aligned Mummy that your player shouldn't complain about.
4) Consider having a talk with the players about what game everyone wants to play. You have a conflict in play style with the "rules lawyer" player. Do the others also want to play "his" game, or do they prefer your approach? Can whoever is in the minority live with adjusting their expectations to what the group as a whole prefers? Can there be some compromise?
Best Answer
If a vampire simply feeds on you (as in drinks some of your blood), you do not turn into a vampire.
If a vampire kills you with its Bite attack (MM, 352):
Ways for a vampire spawn to become a true vampire according to the vampire entry on the Monster Manual:
Or other extraordinary means such as the amber sarcophagus on the Curse of Strahd adventure.
Vampirism is not a disease or a curse, it's a form of undeath. The only way to cure a vampire would be to kill the creature and then resurrect the corpse.