K-tek has the widest range of poles with all the specs for each one. Check out their website for the pole that meets your specs & budget. https://www.ktekbooms.com
Which models? Do they use internal batterys for power? Could the problem be in the unit they are connected to and the 48v phantom supply to the mics? More info needed.
If popping is an issue try mounting the mic with the capsule facing down. Other options to eliminate P pops is to place the off center on a lapel if you’re mounting it on a tie. For other choices look at the Sennheiser line of lavs their MKE 2 or 4 I believe is a cardioid lav.
Sorry it can’t be done. Return the hand mic for one on the same frequency band as your receiver. You do know that you can’t use both the handheld & the lav transmitters at the same time with one receiver?
The Sennheiser connection is not the issue as it will fit in any 3.5mm trs connection. The issue is that that cable is wired for a line level feed, not a mic level feed. While it might work in your situation, I wouldn’t count on it.
You can unscrew the bottom part of the mic to expose the battery. Look carefully at the body and you’ll see a seam that goes around the body. That’s where it unscrews.
About the best camera audio is on the Arri Alexa. 24/48 line in only. Input connection is a 5 pin XLR. It is a bit pricey though at $70,000 for the camera w/o glass.