2006 Range Rover Sport HSE noise (differentials?)

Hello, I'm new to this forum I bought a 2006 Range Rover Sport w/ 135,000 miles about 7 months ago. I absolutely LOVE it! however I have a had a few hiccups since then and I still can't figure them out.

First, when i go on the high way about 55+ mph it starts making a humming noise from the back of the cabin. It stops as soon as you take your foot off the peddle and continues when you push back on the gas. I took it to to an independent shop were they replaced my sway bar (which fixed one problem) and said they checked the wheel bearings and they said they were fine.

Secondly, I went over a speed bump, and a metallic POP POP POP came from what seemed like the back axle (differential?). The speed bump is rather tall and narrow compared to others and it has only happened on that speed bump?!? I came to a complete stop then went and it continued popping, then reverse still a pop. I gently babied it about 1,000 feet with it popping and then it stopped and drives smooth until i'd go over that speed bump again. Awhile back I had a transmission fault message followed by "limited gears available" "HDC fault" and it put itself in to limp mode, however my battery was bad during this time so i got a new one and haven't had these messages since (knock on wood). I don't know if these are connected to the popping?

Thanks for reading any thoughts?