As suggested, play it first "as-is" then see how you feel it runs! You might find your players don't want some of the fluff that comes with prior editions. I played AD&D 2E for a LONG time, then moved to 3rd and Pathfinder. But out of them all, 5th has the most of what we (not just me!) are looking for. Not all (see summary below), and that only comes with actually playing to see what you like and maybe want more/less of.
But otherwise to your points.
1. Short Rest. Recommend against longer rests. Several classes have unique abilities tied solely to the ability to take a short rest, and you're punishing those who use long-term duration spells by gimping the ability to keep the adventuring day going with a "breather." It's really a vital part of the machinery and works well so you spend more time adventuring than resting (especially horrible if you run into random encounters and find yourself resting rather than chasing the bad guy in a thriller). If you're having a problem with the idea of "regeneration" as healing, try and view hit points as abstract concepts of being able to avoid the fatal blow. It hurts the head otherwise to view hit points as realistic measures of damage. If human beings actually got hit as many times as we do in D&D with blades, arrows, spells and giant clubs the size of trees, they'd be dead. Very few "hits" should be viewed as "body blows." Most are "close calls." Even Magic Missile, which never misses, can be viewed as exploding poofs of force that knocked you around but didn't manage to do real damage...this time.
Also, short rests allow parties to exist that don't have dedicated healers, giving players more freedom to play what they really want to play. By making healing take a week, you'd effectively be forcing someone to play a class that heals. D&D rocks because you really can have a party succeed with no cleric / healer bard / druid caster at all. But, it all boils down to "what do your players want more: micromanaging their sleep, or scouting the hobgoblin infested wilderness / looting ancient ruins / schmoozing royalty, etc.?"
2. Proficiency. The more rules you add, the more rules there are for players to forget. This one is the way it is for simplicity. And, unless you're using optional rules that make weapons distinctly unique for what they can do (see Battle Axe vs. Long Sword, exactly the same), there's not much point or benefit restricting too much. But, can't see it being a gamebreaker. I'd try it first and see how it feels before modifying.
3. Rest of the Weary homebrew I've not played this homebrew and had to look it up. But, I have tried DMG's long rests. Didn't work. See above "what do your players want" comment along with "waiting a week to chase down Count Strahd because we had another random encounter really sucks, and wasn't he going to kill the hostages tomorrow? Well, nothing we can do about it because that random encounter sucked my spells dry and I can't get them back for another week."
4. Critical hits This was a big issue for debate in 3rd edition. As to crits, there are more monsters than players. Monsters are going to roll more attack dice. Monsters are likely going to roll more 20s than players. If you have decapitation rules, stun rules, and so on, players suffer in the long run more than they benefit. As to fumbles, a 20th level fighter with multiple attacks has more odds to "fumble" more than a 1st level fighter. Even the Vorpal Blade now only causes instant death using it on a Natural 20 + another Natural 20. In 3.5 and Pathfinder, characters had to "confirm" hits and fumbles, which led to more dice rolling, slowing down combats, and with more rules, turning what would be a 15 minute battle in D&D to a 2 hour battle. This was one of our top 3 reasons for leaving those editions. Be forewarned!
5. Weapon Speeds I'm totally sympathetic because I've liked the idea of randomization and impact on weapon choice in combat, but weapon speeds do suck, just a realization I've come to after decades. Knowing Player A goes first then Player B second and Troll third is boring, omniscient, and leads to predictable play. But, you're going to face a LOT of problems as Weapon Speed is really about Reach versus weight. See the Halberd comment earlier. Currently, I'm using the DMG optional weapon speed rule that is VERY simplistic, and players are getting it pretty well. It leads them to strategize (since you're casting fireball I'll shoot my longbow rather than charge in) and guess at the battlefield. Two reasons we went this route: (1) do away with predictability and (2) limit analysis paralysis as players on their turn try to figure out the perfect thing to do. Because they've already said what they're doing and had to do so by paying attention to what's going on, they're involved. As it stands now, a player can play on their phone and figure out what to do when their turn rolls around. In summary, I'd try out the way it works now and see if you like it before going the Weapon Speed route.
Remember, the quicker combats go, the more time you have to devote to role-play and the story. I can't stress how important this has been between editions for my players.
6. Racial Language Go for it. Anything that makes for a better story should be encouraged!
7. Reading and Writing It sucks to be the only person who can't read, so they just did away with this. Go Barbarians! The simpler way to view might be that if you deem something needs to be written "well" or there's a fairly complex tome to read and comprehend (e.g. a math book that has the solution to a deadly puzzle), you can simply require an "intelligence" check to succeed. Otherwise, see #6.
8. Magic System I'd try it first before barring anyone from getting spells. I know they've done away with "evil" spells so anyone can use Animate Dead, and you can if you want bring it all back. You can bludgeon your enemy to death, burn them with radiant fire, and freeze them so another can slit their throat, but don't cast a spell that animates objects like bones. I'm being a bit facetious but that's really the counter to it all. As for wizards, it's going to suck if they can't take advantage of their classes +2 spells per level, but maybe you could require them to roleplay their study and observation of spells they want to take as they're adventuring. Wizard plans on getting Teleport so he describes from time to time meditating and envisioning his body drifting a few inches forward...and he makes it work, then takes notes as to words of magic he knows that worked and didn't work, and so on.
Summary: D&D 5th plays a LOT better than prior editions. There's a few nostalgic things I miss like having more complex weapons and more complex monsters, and I've fixed those with some DM-vetted material on the DM Guild site. But I only knew what I missed and didn't miss by playing for awhile. The STARTER BOX adventure rocks, and if you haven't already, I'd give that a run, as-is, no homebrew, then gradually decide what does and doesn't work.