Most comments seem to cover the points raised, but one solution with the TV would be to use a scart cable connection if the tv has a scart facility. My Icoms both came with a selection of leads including Scart and 3.5mm jackplugs. I use a Scart downstairs but use the Jackplug in my office so as not to disturb any one.
You can also charge the Icom whilst using it, I do in the car or at home. Just buy any small USB type charger and it can be used to charge’n listen!! I bought two Icoms so they would last all day in the car but subsequently found you can plug them in via the auxillary charger point and a suitable lead whilst driving. I do not know if the batteries are effected by ‘memory charging’ so I always use them until they bleep at me that the battery is low.
I also struggled to hear what was being said in noisy enviroments when using the Icom so my Audio turned the microphone down quite a lot. I hear much better but my good lady recons I tend to talk extremely loadly when I use them on the phone. The moral being that sometimes you just cannot win!