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It won't be long before that happens. It's been possible for a while now to make a mitotic spindle without a cell (mitotic spindle being the thing that splits DNA to put one in each cell.) It's also been possible for a while now to make micelles which are essentially the membrane around a cell which can behave much like cells. Recently the two have been combined, making artificial spindles inside such droplets.

The second part of mitosis (cell replication) is the cell itself splitting, cytokinesis. It seems that people are working on doing that artificially. I've never heard of anyone getting a micelle to undergo cytokinesis, but there are undoubtedly people working on that. And then immediately, someone will hire a postdoc to combine the two to get complete artificial mitosis going.

In vitro replication of DNA has been possible for quite a while too. Someone will get DNA in a micelle duplicating, then dividing by artificial mitosis and artificial cytokinesis. Probably only once at first, since making the artificial cell grow would be yet another complication, but it should meet your definition.

I'd guess it would take about a decade, mainly because a lot of the technical details and hard work will be driven by other goals. The reason people spent time making the spindles in bubbles wasn't to do it, but because they wanted to study how the spindle is sized. There are clear questions one can answer with making micelles divide. I'm not clear why the researchers in the current article did this, but they no doubt had a question to answer, not just "Hey, I bet we can make a cell from plastic." I'm not sure what questions one would be able to answer by doing the full artificial dividing cell I just described, but someone will probably eventually come up with a reason.

I have a PhD in neuroscience.

If you can afford it, apply to take this course: http://hermes.mbl.edu/education/courses/special_topics/mcn.html

It is taught by some of the best in the field, and many alum have gone on to do good work.

To me it seems that they should figure out how the single celled stuff (like amoebae and neutrophils) think before they go on to more complex stuff.

From what I see they seem smarter than most people (including many scientists) assume:
https://www.youtube.com/watch?v=I_xh-bkiv_c
https://www.youtube.com/watch?v=pvOz4V699gk&feature=related
http://www.brianjford.com/a-08-12-infocus_cell-intelligence.pdf

Have our AIs reached the level of intelligence of an Euglypha amoeba, which builds a pretty decent shell for itself: http://starcentral.mbl.edu/microscope/portal.php?pagetitle=assetfactsheet&imageid=26590

It's quite an elaborate shell - with holes in the front and back. The number of "teeth" in the shell apparently is not determined strictly genetically either see 3) in:
http://what-when-how.com/molecular-biology/maternal-genetic-effects-molecular-biology/
Note that it builds a new similar shell when reproducing.

It may be that a single neuron is actually not that stupid and it's because you need redundancy and the ability to control a large creature/"machine" that you have to have many of them and a multicellular body.

I would amplify some of the comments suggesting a non-engineering solution by saying that, if you have not already done so, you might capitalize on some existing programs already extant in the state. Among these, there are or two LTER Schoolyard programs in Alaska. Schoolyard is the outreach and education component of the National Science Foundation's Long Term Ecological Research (LTER) Network. The Bonanza Creek LTER and their Schoolyard Programis hosted at the University of Alaska Fairbanks and, although the Arctic LTER is hosted at the Marine Biological Laboratory in Woods Hole, MA, their Schoolyard Program does have a local component. Each may have ideas and directions you can use.

I would amplify some of the comments suggesting a non-engineering solution by saying that, if you have not already done so, you might capitalize on some existing programs already extant in the state. Among these, there are or two LTER Schoolyard programs in Alaska. Schoolyard is the outreach and education component of the National Science Foundation's Long Term Ecological Research (LTER) Network. The Bonanza Creek LTER and their Schoolyard Programis hosted at the University of Alaska Fairbanks and, although the Arctic LTER is hosted at the Marine Biological Laboratory in Woods Hole, MA, their Schoolyard Program does have a local component. Each may have ideas and directions you can use.

Woods Hole Marine Biological Laboratory has a 4 week summer seminar on Methods In Computational Neuroscience. It's too late to apply for this year, but you might try again next year.

Animals interact with a complex world, encountering a variety of challenges: They must gather data about the environment, discover useful structures in these data, store and recall information about past events, plan and guide actions, learn the consequences of these actions, etc. These are, in part, computational problems that are solved by networks of neurons, from roughly 100 cells in a small worm to 100 billion in humans. Methods in Computational Neuroscience introduces students to the computational and mathematical techniques that are used to address how the brain solves these problems at levels of neural organization ranging from single membrane channels to operations of the entire brain.

In each of the first three weeks, the course focuses on material at increasing levels of complexity (molecular/cellular, network, cognitive/behavioral), but always with an eye on these questions: Can we derive biologically plausible mechanisms that explain how nervous systems solve specific computational problems that arise in the laboratory or natural environment? Can these problems be decomposed into manageable pieces, and can we relate such mathematical decompositions to the observable properties of individual neurons and circuits? Can we identify the molecular mechanisms that provide the building blocks for these computations, as well as understand how the building blocks are organized into cells and circuits that perform useful functions?

Core presentations in weeks one to three will be given jointly by theorists and experimentalists who have worked, often together, on the same problems. In the first week, to supplement the lectures, there will be numerous optional tutorials covering topics including dynamical systems, information theory, UNIX basics, and simulation using NEURON, MATLAB, and XPP. As each week progresses, the issues brought up in these presentations will be explored in laboratory demonstrations and exercises that invite the students to follow and generalize from the paths outlined in the lectures. Exercises involve both quantitative analysis of experimental data and exploration of models through analytic and numerical techniques. To reinforce the theme of collaboration between theory and experiment, exercises are often performed in teams that combine students with theoretical and experimental backgrounds.

The fourth week of the course is reserved for student projects. These projects provide the opportunity for students to work closely with the resident faculty, to develop ideas that grew out of the lectures and seminars, and to connect these ideas with problems from the students' own research topics.

This course is appropriate for graduate students, postdocs and faculty in a variety of fields, from zoology, ethology, and neurobiology, to physics, engineering, and mathematics. Students are expected to have a strong background in one discipline, and to have made some effort to introduce themselves to a complementary discipline. The course is limited to 24 students, who will be chosen to balance the representation of theoretical and experimental backgrounds. .

I doubt aliens (organic ones at least) would have electronic-like displays integrated into their bodies.

Really? How about these? Or these?