@love_leeloo First... Leeloo... Awesome name! The female protagonist in The Fifth Element. Orange hair sorta like a Basenji. Love it!
To your issue. I'm not a vet, I'm not behaviorist, I don't play one on the bloody TV, I'm a Basenji person. So, these are just like... my opinions.
I've had three Basenjis so far and my current male, Logan, is absolutely obsessed with food. More so than any other dog I've ever had, not just Basenjis. There are pros and cons to it. Pros are that he will do just about anything for a snack. He knows the word cookie, so the majority of the time recall is a snap if he's within ear shot. The con's... weight gain, resource guarding, constant scavenging... come to think of it... pretty much everything you've mentioned.
I'm not really too worried about it though. I weigh him weekly and adjust his diet as needed. I've found that kibble is THE biggest contributor to weight gain or loss. He's a big ol' lovable teddy bear with sometimes irresistibly sad Basenji eyes, and that makes It hard not to give in to his snack demands. The good news is that like Leeloo, Logan will eat just about anything. I take that back. He HATES the smell of oranges. Hates it. Steamed cauliflower is my goto. It satiates his cravings and hardly has any calories. Something like 25 per 85g. It's nothing. I've also begun chopping or grating carrots for him too. Others are broccoli and brussels sprouts. Obviously the theme here is vegetables. I no longer give him any kibble of any kind for snacks or training. I've gone to Primal Treats - Buffalo Liver Snaps. The ingredients are: Buffalo Liver.
As far as meals... he eats twice a day, but I've had to cut his kibble back from a 1/2 to a 1/3 cup at each meal. There's a lot more in each meal other than kibble, so he's not being starved. Although, if you asked him he'd tell you that he is. I pick his bowl up as soon as he's done otherwise I have to listen to the bowl rattle for 10 minutes while he licks it. I cannot feed Logan near Sparkle. He'll inhale his, then chase her off so he can eat what's left of hers. They eat separately.
He constantly scavenges on walks. I've had to dig a few bones out of his mouth when he's seen them before I did. I almost never have to worry about this with Sparkle.
I don't know if it's a disorder or normal. It just is. It's not like I can reason with him and I want him to be happy. So, I just have to manage it. Again, vegetables. Get a bunch, find one she likes, and like @elbrant said, lightly steam them.