Two Rules Clarifications, Explaining Recoil and Hacking Limbs Options

[JFixer]

I've been running this game for three days (as in, straight) with an imperfect understanding of the rules. I'm going to finish out the /weekend/... It's a holiday weekend and my paper-game group split up, so we've picked up Shadowrun. I played back in 1e, and that was... a long time ago. Can you help me understand how things work now? I grasp magic, I have a fair understanding of combat, but hacking is still... hard.

1. RECOIL: My player's Sam runs with a Ares Stone Medium Machine Gun. He has 3 recoil compensation modified into the gun. He has an agility of 8, a skill of 6, and the appropriate medium machine gun specialty, as well as a smart-link. He fires two short bursts on the first initiative pass, a long burst and then a short burst on the second pass, and suppression fire on the third. What are his dicepools?

2. Our decker (or, for that matter, my Technomancer in our online game as I struggle to learn a new archetype...) often wants to hack people's smart-links or commlinks. How does she go about doing that? I maintain it's necessary to hack the commlink first, as it's all slaved through that any way you slice it, and that requires an Electronic Warfare + Sniffer (4) test, and then she has to use Hacking + Edit to change programming, or Hacking + Command to give the smartlink a single order. Is that correct? What if she wanted to be able to hack someone's cyber-arm to reach out and touch someone.. or punch someone... or shoot someone... Is that even possible? Step by step, what does these attempts entail? Reading the matrix section makes my nose bleed, I swear...

-JFixer
Old Newbie Judge