Casters having to wait a week to recover spells isn't like any edition of AD&D that I've experienced; 'sleep to get back your spells' is extremely traditional. If you want to use that to make adventures progress slower it's a standard variant rule, and will result in a slower game based around an adventuring week instead of an adventuring day, which may work for you. But it's not going to make anyone think "oh, casters needing a week of rest to recover spells, that harkens back to classic versions of the game!"
The proficiencies with a really limited number of weapons is a weird gamey thing that has never made a lick of sense. The idea that a warrior who spends his time training to use weapons would be adept at using a footman's mace but clueless using a slightly smaller horseman's version of the same weapon, or that he'd be good at using a full size spear but befuddled by a javelin. I urge you not to have things include like this in your game: "Oh, I see you're able to use a long sword and a broad sword, but you're completely befuddled by the slightly smaller short sword and scimitar, or by a dagger. You'll need to spend months training to learn to use them" or "Oh, you're good at using this long pole with an axe blade on the end, however what you've found is a long pole with an axe blade on the end AND a spike on the opposite side of the axe blade, it will take months to learn how this weapon works".
The idea that someone with a dagger will have an initiative advantage over someone with a sword is another hilariously unrealistic artifact from old D&D. If you want to see this in action, make a couple of mock weapons out of dowel rod, pipe insulation, and electrical tape, then get someone to go outside and spar with you. The guy wielding a sword-length weapon is going to have a much easier time scoring hits than the guy with a dagger-length weapon, he clearly has the initiative both in terms of striking first and controlling the fight. If neither person is exceptionally more skilled or athletic than the other, then the dagger guy is just going to lose over and over again. Again, I urge you not to preserve unrealistic oddities from old game systems for the sake of preserving them.
Critical failures implemented as 'if you roll a 1, bad stuff happens' are also weird gamey things that aren't part of traditional D&D. They bias the game towards casters over melee unless you also include critical spell failures, and have the really weird effect that better melee combatants, who get multiple attacks, end up hurting themselves with their weapons much more often.
