I have a small jane magnolia tree (~3 ft tall). Can (or should?) I trim it to be a single trunk, or is it intended to be a multi-trunk / bush like this?
The answer to your question is really up to you. Jane Magnolias typically get 15 feet high and 12 feet wide and can be grown as either a small tree or large shrub, depending on the area where it's sited.
Probably the biggest consideration of whether to plant it as a tree or as a shrub is the size of the planting site.
If you were to reduce the shrub to a single trunk and then limb it up as it grows so that you can mow under it would leave a canopy maybe 9 feet by 12 feet. Speaking from a garden design perspective, this would be appropriate for a small front yard or any area where you want a tree that's shorter than a building and more than 15 feet from a building - perhaps in a bed diagonally off the corner of a house, say. In such a site, a tree-form would allow you to easily plant and maintain a garden under the tree. This would then let you plant bulbs for early spring interest and small (3 ft height max) perennials (or annuals) for summer and fall interest. Jane herself would provide all the interest you need when she's in bloom :)
Leaving the magnolia in its shrub form will require a larger footprint for the tree, and a footprint that can be enlarged over time as the tree grows. For example, let's say you plant the shrub-form of the magnolia in an open space on your lawn, giving it a generous six-foot diameter edged and mulched area in which to grow. In about four years Jane will have reached the six foot diameter and have started interfering with your lawn mower. At that point, you'd have to expand the bed, probably to a nine-foot diameter. And then expand it again in several more years. Note that I do not recommend shearing a magnolia - they don't like it and look terrible. Alternatively, you could plan for the future by putting Jane in the middle of a twelve-foot (or, better, fourteen-foot) bed and planting annuals around her; fewer annuals each year as her canopy expands.
As you can see, from a design perspective, a shrub-form Jane would be appropriate for only a large area of your yard; perhaps as an anchor to a corner of the lot, with three to five smaller (at maturity) shrubs in a "smile" facing your house. These smaller shrubs could be beautyberry, clethra, itea, or some of the less over-used spireas. Alternatively, she could be used as a specimen in the lawn and would look glorious when in bloom, but that should require a large bed for her to grow in (this makes it far easier to weed and, if mulched with wood chips annually or biennially, would prevent most weeds from even sprouting).
So - look at the size of the planting area, then look at the amount of space you want to give her in that planting area. Magnolias tend to be semi-vase-like to globular when grown as a shrub - do you have that amount to spare for this plant? Again, do NOT plan on trimming her annually. Depending on the time of the year you prune, you can easily prune off all or most of the flowers, and as I noted above magnolias do not like being sheared. Any trimming needs to be done as if she were a tree, trimming branches back to a parent parent branch.