How would life-forms made of energy work?

You cannot isolate pure momentum or pure charge - the idea doesn't even make sense. It would be like asking for a poem that was made not out of words, but pure beauty, or a balloon that wasn't made of material, but pure loftiness. (People might use the imagery of "pure beauty" metaphorically, but you cannot literally have pure beauty existing on its own.) The same is true for energy. You can think of the relationship between energy and physical systems as being similar to the relationship between value and currency. Currency can come in different forms - dollars, yen, pesos, etc. They all have some value and can be converted into each other. But there's no such thing as value itself. Value is an accounting tool to tell you how the currencies convert. Similarly, there are many different types of physical systems - compressed springs, balls at the tops of hills, lumps of uranium-235, etc. They all have energy and can be converted into each other. But there's no such thing as energy itself. Energy is an accounting tool to tell you how the physical systems convert. When people talk about "pure energy", they are at best using a sort of shorthand, usually to refer to photons, but in reality there is no such thing as "pure energy" any more than there is "pure value".

This is a rather problematic question. The physics inclined folks are attacking from the perspective of "how could that possibly work? it can't". I have a physics degree, too, but I'm going to tackle it from a different perspective. This whole idea of "energy-based life-forms" comes out of (a) the idea of a soul, but rendering it as physical and (b) the idea that you could keep subtracting away the physical parts of ourselves, and be left only with consciousness. There is no evidence that you can have consciousness without a physical matrix for it. If it was possible, there is obviously no way for us to detect it or interact with it. Another troubling scifi trope in this regard is the "energy field", which people like to think as, say a fence, that you can only feel when you cross it. Well, a real such "energy field" would actually be a high volume of fundamental particles zooming across a limited space. I.e., that "energy field" is actually made of matter. All energy that you experience comes from matter. There is no "just energy". Light that hits your eyeballs is photons. Sound waves are pressure waves in the air, also matter. Electricity is the flow of electrons. Heat is matter vibrating incoherently. It all requires matter. There is no energy by itself.

The first problem to solve in the evolution of an energy-based life-form would be existing for any very long period of time. Energy normally disperses quite quickly. Matter has the advantage of persisting more, so that the beginning of biological evolution in matter was more concerned with reproduction. Once life's moelcules become very large, though, persisting and staying together is just as much of a problem, so evolution in energy-based life might not be all that different. But how precisely would energy-based biology pass this initial barrier? There are probably lots of possibilities but I see two. One would be for the life-form to constantly travel near light speed. Since light is going to constantly travel at light speed anyway, and elecricity travels at light speed in a vacuum (according to Wikipedia), this seems like a convenient way of keeping the energy from 'running away', provided there is some convenient electromagnetic way of keeping all the energy traveling in the right direction. The other possibility would be to more strongly contain the energy in one place. One way I can imagine this would be of the life-forms live in a substance in which the speed of light and of electrical current is much lower. You would need a lot of this substance. A star seems the most feasible location for energetic life for this reason as well as for the reason that you would think any life on a planet would incorporate matter just because it's there. The speed of light is quite slow in the interior of a star, so persistent forms seem possible. [edit: see comments for discussion of slowing down energy through cooling.] It seems like it will be a long time before we are ready to try looking inside the Sun for energetic life forms. If they left the Sun they would probably travel at light speed and so we could not interact with them for very long! However, energy beings would not be totally invisible, and we could probably figure out they existed through their aftereffects. For example, they would probably constantly convert energy from higher wavelengths to lower wavelengths in order to maintain themselves. They would have to eat energy the way we eat matter.

What energy are we talking about here? There list is finite, you know. (http://en.wikipedia.org/wiki/Forms_of_energy) There is gravitational, "emitted" by all matter in proportion to mass. Electromagnetic energy which is a function of electrical or magnetic charge. It can be transmitted in the form of photons or exist as field surrounding an object, much as gravity does. There is the Strong nuclear force that holds neutrons together or the Weak nuclear force that holds sub atomic particles together. These together make the matter collate and congeal in the forms we are familiar with. And there is also kinetic force, which is really the observation of things in motion , impacting each other with effect depending on mass. None of these really exist as "free" energy that can form complex structures, mostly because they are all tied to matter. Only electromagnetic waves (light, gamma rays, radio waves, etc.) exist in a manner unattached to the existence of matter once emitted. But aside from wave interactions (http://en.wikipedia.org/wiki/Waves), light really interact with the complexity to make a "life-form". Energy can convert to other energies (http://en.wikipedia.org/wiki/Energy_transformation). So far the only means of doing this involve interacting with matter. Imagine electrical energy being converted into a magnetic field because it passes through a coil of copper wire. Or a chemical potential being converted into kinetic energy (an explosion). Also, there really isn't any process known to convert energy to new particles. We have not observed particles like protons, neutrons or electrons coming into existence because of an energy interaction. So far we mostly observe particles and atoms loosing mass (as emitted gamma rays in the measurements done) and in rare cases, seen mass increase as energy is absorbed. But not new particles, such as you suggest in the question details. So I don't see creatures of just energy as being possible in this universe.

Dusty-plasma https://www.newscientist.com/article/dn12466-could-alien-life-exist-in-the-form-of-dna-shaped-dust/

Energy is the measure of the possibility of change, but it is not the change itself. Information is the measure of the realization of change. Time is the measure of change... Assuming that there is a place that holds pure energy (there is a possibility to change something,) a life-form that will work with this energy, will have to be intelligent to hold all this energy from wasting (dissipating in the infinity of space.) This life form will be unique, else will dissipate itself in infinite small pieces, and will be immortal as long as it won't procreate (dissipate.) Its goal will be to keep all that potential together and may start multiple time lines by failing to keep it in balance either by dissipating all the potential or reducing its space to the original point. With each fail will suffer grate pain but also will learn and perfect itself for the next iteration... Well, I'm confuse - I don't think I can really understand this... Maybe it cannot exist at all!