I have no problem seeing your image. It is a nice plant. However, I'd like to ask something: If the spot where you took the picture is where you keep the plant on a regularly basis, where is the light source? Is a window nearby? In the picture, it looks like a rather dark area. If so, it might be too dark for your plant to thrive. Always remember, plants use light to make food (photosynthesis.) If one doesn't give plants enough light, it is like starving them to death.

There is no difference between stem tissue and branch tissue. They are the same & equally likely (or unlikely) to root. I also think trying them directly in the ground where you live will be very unlikely to yield results. Besides, the plant will prefer full sun and you'll not likely be able to root them in full sun, so you'd need to shade them or move them if the did happen to take. You should use a very coarse and sterile mix for rooting. Perlite, Turface, a combination of perlite and Turface, or any combination of chopped sphagnum moss (not peat moss - chop it in a blender or food processor) and either/both of the other two ingredients is particularly effective. If you use the coarse ingredients, soil volume is of no concern and a greater volume is easier to keep damp (but not wet). A spot with open shade is best (in shade but on the north side of a building or fence with open sky above). DO NOT fertilize cuttings until well after they've struck. Fertilizer inhibits water uptake (which is critically important to cuttings) and slows root initiation. Al

Your plant is a Peperomia obtusifolia, aka 'Baby Rubber Plant'. But that name is a bit unhelpful as 'Rubber Plant' usually denotes Ficus elastica and until I saw the picture I thought you had a baby one of those ;-). They are very easy to propagate just by cutting pieces off at a node and inserting in growing medium, or even a glass of water. You'll find plenty of help if you have more questions over on the House Plant Forum which is much livelier than this one. Here is a link that might be useful: House Plant Forum

Do you want the good news or the bad news first? Since the bad news isn't all that bad, I'll give you the good news. A) When the time is right, it's going to be really easy to cut your plant back, which B) will allow you to be rid of the rigging you're using for support, and C) you already have branches in place to cut back to. D) If you want to separate one or more trunks from what a bonsai practitioner would call a 'clump' or 'grove' planting, it will also be very easy if the part you intend to separate has roots attached. And, if there are roots attached, you should be able to be close to 100% sure of a successful operation. You'll find, though, that you aren't going to need to cut back if eye appeal is your concern. You'll end up with a very attractive composition. Now, the bad news is so bad it almost scares Chuck Norris. Just kidding, it's not too bad at all. If you wait until next June to do the work, we'll talk about a plan if you're interested, you'll be richly rewarded for your patience. Your tree varies in strength throughout the growth cycle. It's reserve energy supply is currently declining and will continue to do so until April, reason being, the shortening days and diminishing light intensity. Somewhere in the neighborhood of Father's Day or the Summer Solstice, your plant should be peaking both in it's level of stored energy and its current ability to make food. A tree's food is the glucose/ sugar/ carbohydrate it makes during photosynthesis. Longer days and brighter light = more light energy striking the leaves = more food production. Trees full of stored energy and currently at peak production of photosynthate/ food respond with a whole lot more enthusiasm when chopped back or repotted than trees just getting by. Also, if you prune now, ALL growth the plant puts on between now and Memorial day will be somewhere between somewhat to very leggy, and you don't want to save that growth. If you cut it back in June, all growth (until fall) will be quite compact, which is what you do want, especially when the tree back-buds as energetically as F elastica. The idea is to remove the long growth in early June, wait for 2 leaves to grow on each branch, and, when the 3rd leaf is about to open, pinch (prune) the branch back to 2 leaves. This is the formula for rapid ramification, which translates to leaf and branch density. So, prune in June, then pinch branches for the rest of the summer, then allow the plant to grow unencumbered by pruning all through late fall, winter, and early spring, repeating the cycle every year. If I want to split this one trunk from the rest of the plant, what would be the best way to do so? Should it be done at the root? Yes, at the roots. Be sure any trunk(s) you're removing has/have roots attached. If not, I can help you make roots grow so you can separate the trunk next year. The process is called layering and I use it all the time to layer trees off of their own ugly root system and force them to grow new roots. The tree you see below has been layered off of it's old roots, which were cut off just below the wire used as a tourniquet, which is still attached. Al