> Build a database for biology.
Better than Entrez/NCBI? They have a ton of data. Yes, not particularly user-friendly in the way the web community might be used to, but it has all of the data and biologists know how to read it. What would you add? (Yes, there's a lot to add -- but it's not a matter of a prettier UI, and NCBI does have an API already that people find usable).
> Reading DNA in vitro
What does this mean? Sequencing DNA without extracting it from a cell? Why? Sequencing is largely a solved problem now. Costs are dropping faster than Moore's law, and there's literally a thousand vendors who will do it. Even synthesis is advancing so fast that people are beginning to talk about not doing subcloning anymore and just synthesizing the entire construct! (Note that just because we can synthesize kbp oligos now doesn't mean that they're biologically useful in much other than bacteria and yeast, though... pesky things like epigenetic modifications and nucleosomes/genomic DNA packing... among others.) Also, the extension of "writ[ing] DNA sequences into plasmids using the capacitance of the cell wall via [a] nano tube" seems a bit far from current technology.
That said, I think these are important problems and I'd love love love to see more people working on them versus more web and iphone apps! This was not the list I expected to see, which is awesome. But the biology-related ideas don't come across as being communicated with much sophistication.