What kind of technology is required for plant seed DNA printing?
As Chris mentioned in his comment, 'printing' DNA from scratch (i.e. synthesizing a long strand de novo) is expensive and difficult. Unfortunately, the process of GMO creation is not as simple as assembling a beautiful DNA sequence on the computer, printing it, and then inserting it into a cell. Here's a related question about de novo sequencing. Plant biologists, please correct me if I'm wrong but I don't think it's a trivial matter to grow a plant from a single cultured cell.

Your third question reminds me of DNA programming, which is an amazingly cool, developing field. Many companies (including Microsoft) are funding research into DNA circuitry and biological computing, making computers out of biomolecules. Here's an interesting paper that will tell you more. What you may be most interested in is the branch of DNA programming that seeks to identify discrete protein-coding and otherwise functional DNA that can be utilized as a sort of "programming language" to build a new organism. One of my past supervisors recently joined this field and I'm a little jealous. Overall, this is a very new field so there is much to be accomplished and very little is technically possible, although the principle of GMOs is really just an optimization of an existing organism.

In summary, the answer to all three of your questions is: No, not very well. But we're trying.

Most likely this isn't something you'll be able to pick up in your spare time in order to have a cool plant to grow on your fence. It's very expensive and very difficult (in some cases, maybe even impossible). However, there are so many unknowns in this area of research and everything you propose is reasonable in theory. Let me know if you figure it out. I would love to code my own garden.