See, I call it "lazy viewing".
I APPRECIATE the fact that they don't resort to trek-speak to handwave stuff, and I appreciate even more that they don't roll some 'lowest common denominator' exposition boy out every couple of minutes to explain the obvious. The writers are trusting us to keep up. They maybe gave their audience too much credit this time out. Alas.
The Patch: Flight suit material for space pilots. It's OBVIOUSLY vaccuum rated. Even modern day fighter pilot pressure suits are so loaded with plastics and polymers they'd probably suffice. Never mind a SPACE Pilots. Doesn't have to be a perfect seal on the planet. Once in space, presuming there was some backing (say a rock and some duct tape), vaccuum would provide a more or less perfect seal. Good enough for her purposes anyway.
_I_ could patch that hole with those materials. I need Geordi Laforge to mumble on about differential pressure in the flux capacitors?
Flight Controls: OBVIOUSLY mechanical linkages (levers etc) intended to be manipulated by the original pilot's musculature (like thigh bones). The writers WERE explicit enough to remind us that only four controls were required for basic flight. They SHOW her manipulating them (hands and feet).
Air Tube: It's OBVIOUSLY a flesh and blood critter. Blood as in an 'oxygen transportation medium'. Probably engineered from a mammal - Human, most likely (demonstrated expertise from building Six et al). It OBVIOUSLY needs air every bit as much as we do. They even gave us an Oxygen detector to exposit the fact that it was air...
First thing I thought of when she opened it up: ("hey! It bleeds. It's gotta have air somewhere...")
Aside: This human or animal origin probably explains WHY the controls were physically situated where they were - to take advantage of existing nerve and muscular structures.
Duct Taping the Wings: 45 minutes of air shown on suit. A fresh supply of air provided. Duct tape explicitly shown, 40 odd hours not accounted for. Pick any of about ten plausible opportunities.
Finding her way to the BSG: Grab altitude, mentally review BSG SOP, establish a polar orbit (or whatever orbit is most likely to stumble across the BSG platforming for search and Rescue operations). Get lucky.
NOT Lazy writing at ALL: They SHOWED us all the equipment needed, and enough context to know what it could do. They spoon fed us flight controls (cause not everybody knows that only four controls matter). We can infer off screen capabilities and actions based on what we know about the characters involved. They left out out redundant exposition and fatuous handwaving, and they left IN all kinds of STORY...
LOVE this show. And NO, actually, I DON'T see a lot of good TV...
But somebody please explain why people from Kobol wear neck ties? Now THAT'S inexplicable...
A'Mal
You can't seal against the vaccum of space with duct tape. Duct tape isn't even water tight, let alone air-tight...and definitely not at that kind of pressure differential. A rock? Give me a break! 
