I can usually train in 3-5 days and average 200-350 BE a day, so maybe I'll be able to answer some of these questions?

Terrain/Level: Forest 2 is definitely the best. Even in winter, there's a good amount of prey. You also get a lot of empathy encounters here, which give +5 moves when your wolves succeed. Also, the only predators here (besides event ones) are foxes and badgers, so your wolves won't flee too much.

Wolves: CP helps a lot when training. Resolve and Empathy are the main ones that speed up training for me and Battle never hurts. Of course, battle boosts will get through training faster, but it doesn’t slow you down too much if the wolf or wolves don’t have a boost. I'm not sure what others do, but I take the wolf or wolves I'm training and fill the other spots with wolves on defensive moves. The extras take most of the damage and your trainee(s) last longer. Usually, I train 1 or 2 wolves at a time, but the number you train at once is up to you. From my experience, 3 or 4 wolves at once slows things down by a few days, because BE isn’t being gained as quickly.

Supplies: I usually but 5-10 Chinese pottery at a time and a few health potions. I agree with what Frigid said about buying as you go. You can make a decent profit from Forest 2, so you'll be saving yourself som mush by doing this. The empathy CP I mentioned before also saves you a lot of mush if you have enough to win the encounters. Also, don't forget to bring those mushroom and berry snacks, since those will save you a lot of time.

Other: I'm usually training for 3-5 hours a day. Depending on how many wolves you're training and how often you're online, the tips above should put you around 3-5 days for DG. Other trainers may do things differently, but these are the things that have been most effective for me. I hope this helps and sorry it's so long!

BE training on average for me takes a total of 3-5 hours. If I work hard at a wolf, I can have two done at 925 by the end of the day, but I don't do that anymore since I haven't the time!

I use the one DG one trainee method. Any more than one trainee and I find training is painfully slow. The DG will (preferably) have the maxed Big Six traits: battle, resolve, agility, stealth, perception, and luck. In my opinion, all are absolutely key to exploring, as the first three enable your wolf to adeptly take down prey and enemies, and the last three enable your wolf to actually find additional prey on top of predators, which will make or break your mush return when buying explore moves. Note: while training, be prepared to lose mush. Don't worry: when your wolves are finished, they'll make up for what they cost you more than tenfold. I use a LW(97lbs) DH DG as my trainer, as they will be able to take more hits, and since their offensive ability will not matter, the LW gives them an agility advantage to dodge attacks.

The trainee will have battle, resolve, and agility maxed out. At least max battle is necessary, since any less and your wolf will usually not be able to one-shot rabbits and squirrels(which is integral to training and prevents prey from fleeing half-dead). I set the DG to a defense move, and the trainee to offense. The DG will split attacks between the trainee and themselves, as well as help find prey for the trainee to kill(but only if the DG has SP&L).

For terrain: I really like forest 2, because prey spawns instantaneously and I don't like spamming the stalk button when tracking. I don't touch a lot of the other low forest levels because of this. A lower level also means higher chances of digging up goodies like health potions, and a lower level of SP&L to find prey. It might have a lower amount of enemies, but if your wolves are properly equipped, the prey should more than make up for it. Each forest 2 level earns around 100+BE, so your wolf should be done in 9 levels(3600 moves) or less. I highly recommend purchasing at least 100-400 chinese pottery per run.

Extra tips: Make sure not to level up while replaying a level! This will screw up your current level, and make it so that you cannot kill any prey or enemy. Also, I would not advise you to go crazy buying explore moves before you have a basic explore pack(Big Six traits maxed and at least Neck Snap 525BE). This can lead to you losing mush instead of gaining mush. Once you have a full fledged explore team, you should be earning 200+% mush back.

I hope this helped!