1. what is the Response rating of the drone? I am lost - is it the response of my 'link (because it is what I use it to jump in) or is it drone's Pilot rating (eventually +/- Handling)?
When jumped in, you use the response of the drone, which should be 3 for regular drones, 4 for security/restricted drones, like the doberman drones, or 5 for any military/forbidden drones (of which you have none.) If you're using the Command program and remote actions, you use the response of your link.
Anyway, for the blimp, you'll have a response of 3 and an infiltration skill of 2. However, the rules on vehicle sensors (from the vehicle combat section) say:
Since vehicle stealth
is limited by the driver’s ability, the dice applied for Infiltration skill
should not exceed the driver’s appropriate Vehicle skill.
So, that's 4 dice for stealth unless you're running hotsim, then it's 6 dice. Hell, I'll even give you the control rig bonus for another +2.
That'd make it 6 or 8, cold or hot.
2. what rules are you using for Data Search?
The base book rules. It's an extended test with info on 6, 12 and 24 hits. Each test takes a minute to accomplish because you're searching the whole matrix. You've got the electronics group at 3, which gives you a data search skill of 3. You've also got a Rating 3 Browse program which is 3 more, and there's +2 dice for using hotsim, which I threw in, because, hey why not? If I'm rolling for you, you don't have to worry about things like solar flares killing your satellite communication and giving your dumpshock.

So far I've given you the 6 hits info. Just the basic public stuff. We'll continue on a little and, if you want to keep searching, you'll get the 12 hits stuff.
The way I do extended tests is a compromise between "auto success" of infinite extended rolls and the "you need 12 dice to do a basic thing" horsecrap of diminishing dice pools. I say, you can roll as many times as you have dice, because, after a time, your resourcefulness will reach its limit and you'll run out of tricks.
3. @IC leaving the Doberman on guard, I should've known my body is being carried
I figure coming back to your body is always a slightly disorienting circumstance, even if you know where you're going to be.
By the way, you've got about 10-15 minutes worth of actions built up with all the recon and data searching while the guys are conversing and planning. I'm not too certain exactly when things are happening, but it doesn't really matter.