Can they charge after they deep strike?
Yes. I mentioned that they can make disordered charges out of Reserve, that means they can declare charges but not get any charge-related bonuses. If you play Dante as your Warlord they scatter 1D6" to boot and nothing in the BRB says it counts as using your jump packs as moving if you Deep Strike, so precise scatter and re-rolls charging. He can also generate a second Warlord Trait off the Strategic table if you're playing that sort of match since he's so old and wise (and a fucking bad-ass with an AP2 I6 power axe).
Also need how to deal with the void sheild generator, ignore it and kill everything inside or go attempt to pop it?
No experience there, no idea even what the rules are for it. What does it do on the table-top? Can't say I've ever had a problem nuking something but I play BA and there's melta and power fists everywhere in my army. I tend to always get close enough to use them