Really? To heat and melt sufficient ice around 25km of cabling? I don't know what temperature this ice is at, I think on the surface Europa averages around -300F, so it's probably at least that low. I guess a lot is going to depend on whether you're fine with the ice refreezing around the cable - if the ice shifts at all, the cable breaks. Keeping the whole thing heated continuously seems implausible
No, not really. Water is very effective shielding, and you could melt a base station through the ice and do exploration with subs it sends out if you want fairly pristine samples. In the Jupiter system, it's also hardly the biggest radiation source around.