To answer the question about the charging current: As far as I know, all Teslas (and probably all BEVs) have limits on the charging current as one approaches full charge. And, interestingly, the charging currents at those high SOC (State Of Charge) are the same for both L2 and Supercharging!
Take a Supercharging M3. at a Gen 3 SC that can do 250 kW, and say that the car is at 5% SOC. One will get 250 kW until the car's at 25% or so, and then the charge rate will typically taper off linearly with increasing SOC. At 50%, it'll be around 100 kW. At 80%, it'll be around 60 kW. At 90%, it'll be around 20 kW, and, as one approaches 100%, the charge rate will drop into the single kW.
Same thing happens with L2 charging, but typical L2 for Teslas is 240VAC @ 48A, which is 11.52 kW. That will run like that to 90% - but when one gets up a bit, the rate drops off to the same numbers one sees while Supercharging, in the single kW or less as one approaches 100% SOC.
As it happens, this is all about protecting the battery.
If one is messing with NIMH batteries, Tesla strongly suggests, with good reason, keeping the day-to-day max charge to 80% or so in order to get improved battery longevity. Their words: 100% isn't forbidden, especially when leaving on a long trip, but the idea is to not sit there with 100% charge for long periods of time.
With LFP batteries, Tesla actually suggests going to 100% on a regular basis. Part of that is because the battery chemistry can handle that without much degradation; part of that is because the Battery Management System (BMS) needs to see 100% from time to time in order to get an accurate idea of how much charge is actually in the battery.
Final note: When one is going on long trips with a Tesla and hitting multiple SCs on the way, Tesla's routing software (and also A Better Route Planner's software) will strongly suggest not going to high SOCs; because of the slow-down in charging rates at high SOCs, it's better, in terms of overall trip time, to charge to a somewhat lesser SOC. Unless there's a big gap to the next SC, or the possibility of skipping an SC charge, given one's route.