Well, for the typical ebike, you're unlikely to be drawing that 40a more than momentarily on startup most of the time, unless you have a lot of hillclimbing to do. The typical 48v40a system is around 2000w max power.
I can't say how using that continuously would affect the battery, as you don't state the capacity or any other battery specification other than "48v", which usually means 13s of some type of Li-ion or Li-po. But let's assume it's a typical "2C" battery, so a 20Ah. If so, then that means at 40A it would last about half an hour, and the battery would probably be pretty warm inside. If it's a 10Ah, it would only last 15 minutes. And so on. (realistically you'd probably get less runtime than this, as most of the cheap ones don't actually provide the full capacity under significant loads).
But the wires would not likely be noticeably warm, even if they were 12awg, unless they are tucked away from all airflow inside thermal insulation of some kind.
You'd have to give the complete specifics of the use case to determine if you really need that thick a wire or not...but i expect 12 or possibly even 14awg would be sufficient.
Some examples:
I use 10awg on much of my SB Cruiser trike's battery wiring, and that sees peaks of 100-200A depending on the experimental controller setup du jour
, and continous of about 18-20A, depending on conditions. I've never measured the actual battery wire temperatures, but I have handled the wires immediately after a ride, when testing high loads so high currents frequently, and even the ones that run thru the styrofoam-insulated cargo compartment from the battery that's in there to the breaker and cutoff switch, and then to the controllers, don't feel any different than ambient.
The 12g and thinner wires on the *phases of the motors*, which see way higher currents during both accleration and regen, now *those* can get hot, and even the 10g solid-core phase wires on one of the motors will be higher than ambient (but not hot). But those currents are several times that of the battery current, for the same periods that the battery current is high.
Regarding connectors themselves, there are a number of good threads around here that show and discuss connectors for various use cases, that may help you decide, but it *is* a lot of poking around and reading.
Myself, for higher current applications, I use the SB-series Andersons, typically the SB-50, mostly because I already have them salvaged from other things, and so far there hasn't been anything I've used them for that exceeds their capabilities, and they are genderless, and the salvaged ones I have usually ahve 10awg already in them, sometimes 12awg, occasionaly 8awg. These are two-contact connectors, but there are three-contact variants, and you can get keyed housings that only fit others with the same key, so you can't plug wrong stuff together when you have several things using these.
Anderson also makes larger and smaller connectors like the PP series, which can be ganged in whatever number and configuration you like, as the housings interlock. The PP75 uses the same contacts as the SB-50, which easily hold 10g (even 8), and in fact will mate with an SB-50 housing. You can key the housings by putting some at different rotational increments, to achieve the same effect the other housings achieve.
They also make connectors that have multiple large-contacts for high current, along with multiple small contacts for low-current, that could be used for phase/hall setups.
But all of these are rather large, as a single contact for the SB50/PP75 is about 2/3 the lenght of my pinky finger, and perhaps 1/4 the volume. The entirety of a PP75 including housing is a little larger than my whole pinky. So they may not be what you're after.
They are also open housings, so definitely not waterproof by themselves...but Anderson does make waterproofing bits for them, and they also make panel mounts for them (though you can make your own panel mounts for the SB series as they have two bolt holes thru the housing to secure them in various ways, including to T-handles that allow quick easy yanking-out if necessary).
For halls I have used many connectors, and never found one I really like--they all have more disadvantages than advantages in my application. So I usually solder or crimp them permanently together. I usually solder everything on a bike, except for the battery connections, once I have it all worked out and am finalizing the wiring setup.
But the best of the ones I've used have been things like a micro-usb extension cable, cut in half. One half goes to the motor hall wires, and the other half to the controller. The plug fits thru most of the hubmotor axle nuts I've dealt with, so it can be easily pulled thru without cutting anything for various motor or wheel repairs, if necessary. It's not waterproof, but filling each half's slot with dielectric grease, plugging htem together, then coating that with more of it, will keep water out of it. If you also slip some heatshrink over it before plugging in, and fill that heatshrink with teh DG, and then shrink it, it not only keeps water out, the heatshrink binds the connector together so ti can't accidentally be unplugged. But it's easy to cut thru for a roadside wheel repair if necessary.
The old PS/2 connector also often fits thru axle nuts, but it *requires* something to bind them togehter (like the heatshrink) becuase almost any vibration *will* unplug them.
The Cannon connectors (like you see on aircraft equipment) can be made waterproof easily, or bought that way, and are very sturdy and will not come apart accidentally (they have lockrings)...but they are quite large for the number of connections, and expensive.
There are a number of variants on the XLR connector that have enough pins for halls, but not waterproof (can be made so, though), and are also large.
The Higo / Julet connector systems are waterproof, small, and not all that expensive, and the higo comes in overmolded with cable, and panel-mount types.
