Quick and dirty summation of this.
1) If you have a 5 RES and you take a 0.1 essence hit for cyber (essence 5.9), you now have a 4 Res.
2) once you have already taken that first hit, you can now go ahead and lose as much essence you want, up to 5.0 (so another 0.9 points available for lose without further Res losses.
3) AT ANY POINT after you lose that first bit of essence, you can spend Karma on Res making it a 5 again.
3.a) If you had a 6 Res, took a data jack and then had a 5 Res as a result you can STILL spend Karma to bring it back to a 6 (it doesn't lower your max, just your current).
Now, as the Res question has been answered, here's a couple of things that make a TM WILDLY better at hacking than a Decker.
1) Diffusion of Firewall. need to hack? Hack away with the system losing as many hits as you got in your roll (net hits). Firewall is the defense for almost everything you'll be doing, so...yeah, nice. Oh, and btw, it's an UNDETECTABLE modification to his stat. So the system/Decker is unlikely to swap his stats after you do this.
2) Infusion of Firewall. going to get into it with a Spider or Decker? Infusion of FW boosts your FW rating. Again, as most offensive actions that you'll encounter in cyber combat are defended with FW, you'll have better defense.
3) Transcend Grid. Must have. Good effect, low drain code. You can always thread it at level 5 with no harm for yourself. It removes the penalty of the Public Grid. That's very useful.
4) Puppeteer. This one is much easier if you push the limit with edge. Then you can use it at level 1, so the fading is only 5. If you get 3 net hits on the oppose test it mean you can tell the device to invite marks, which can instantly give you 3 marks on a device without you being seen by GOD or even by the device's owner. Very powerful. In combat, you can make a Decker Data spike HIMSELF if you get those 3 hits. Remember, the owner of a device/persona automatically has 4 MARKS on those items (data spike would mean an extra 8 to his attack on himself...ouch)
5) Resonance Spike. It doesn't build up OS, also it doesn't count as an attack action, so won't notify the owner. So if you need to stealthily brick something, this is as good as it gets. Fading is a bit high on it though, making it less reliable than normal data spike. BUT, if you can see it, you can attack it. In a combat, you can brick a set of cyber-eyes and give your enemy a -4. Good for boss fights where the Big Bad is a sam.
6) Cleaner. Must have. As far as I know, this is the only way to modify OS.
Ah, you say, but some of those are sustained CF's and you'll take a negative. True, BUT, you can have a sprite sustain those CF's as a simple action and it only eats 1 favor for every (Sprite Rating) rounds. On top of that, you can have your sprite ASSIST you in the treading of the CF in the first place, adding (Sprite Level) in extra dice for your roll (Rating 6 Sprite helping a Resonance Spike would be kinda nifty)
There's a TON of things a TM can do that a Decker can't. And for the record, a TM can do EVERYTHING a Decker can do (except be PART of PAN, though he can defend it still, and with Infusion of FW, he can do it better than a Decker.)