I just realised I could post as a guest on this board, so I'm going to take advantage of it.
Well, I can't exactly say I appreciate it. Unless you feel your life is in danger because of revealing yourself, I really can't see why not to use a name to identify yourself. It isn't like anyone is using their real name here anyway, so what are you buying by just posting as "guest"? I'm not saying register if you don't feel like it, besides the email addresses of people are hidden(or can be by personal preference settings). I seem to have plenty of people that register to see if they can get into the locked sections, and when they can't they give up and never show up again.
I guess it comes back to the original question, who are you hiding from?
how many different types of energy are there
As many as you can come up with names for.

Seriously. Everyone is working independantly from each other for the most part and come up with their own names for the same or different things. It also depends where the differences in properties matter, so they decide it needs a different name.
In true essense, it's all the same, but in the same way matter is all the same, meaning the atoms within matter all have eletrons, protons and neutrons. In "energy" cases, it's all under the classification of "magical energy" to differenciate from kinetic energy, or heat energy, etc. Magical energy is found in many forms and combinations, much like you might find copper ore (which would be copper with impurities), or smelted copper (pure copper), or an alloy of copper and some other pure metal to get different properties. This is why there seems to be different types of magical energy, went in essence they are all the same.
The properties could be considered by "Frequency" (I hate to use that word, but it will make more sense to you based on your apparent backround), density, and mixture. Frequency might be considered "color" (which is arbitrary based on personal symbolism). To some it's easier to filter between these "colors" rather than covert, but both are ways to extract a "type". Density is how "energetic" a "volume" of energy is. For example, if you had a 1 inch cube of foam versus a 1 inch cube of lead, the lead is much heavier and denser. Energy can work the same way, denser energy seems to have different properties than less dense energy. Just like you can build a reliable car out of iron, but you really couldn't out of foam. Certain applications of magic require that type of density and strength that more dense energy gives. (I'll get into this more in a minute). The last would have to do with mixture, simular to alloys that I mentioned before with metals. By combining different densities and "colors", in different orientations, patterns and proportions, you can get even more unique properties. Kind of like we are using ceramic as armor on tanks these days, because it's a mix of lots of different things to make it useable as armor, but you would never think a "cousin" of your ceramic plate your eating off of could be used in a such a way.
I know of the 'basics', such as Psi, Chi, Kundalin,...
Well, 'basics' is a matter of point of view.
Psi is simply a basic subset of magical energy. Meaning a certain band of "color" that I mentioned before. Psi is effectively the same as the ambient energy that is around you, just a narrower band of what is possible. Some believe that psi is a natural product of the human body, which is false. Life energy is, anything more than that is the individual converting life energy to whatever else because the individual user wants it that way (because of dogma or otherwise). (I've proved this time and time again to the different psions that have joined up).
Chi is "life energy", which is unique to the person. Life energy is generally far denser than ambient energy or even the resulting energy one might get by conversion (ie. to psi or whatever else). It also is "textured" or alloyed unique to the person. This is because the person's spiritual systems produce the energy in what I call the "soul reactor". It's the "flavor" it produces is very unique to the individual, and all of their systems are specifically designed to run off that energy. However, as that energy gets distributed from the source, it gets more "waste" material or is simply more broken down, so by the time it reaches the outside, it is NOWHERE near the potency or density that it was from the source. However, since your body is tuned to this energy, you can do the most with it. However, obviously, it's a more limited source than ambient energy (which is basically the great mix of waste energy of you and everyone/everything else). It's "limited" because your spirit runs on this stuff, and if you use it elsewhere, your spirit doesn't have it to run it's own systems if you use too much. Much like if you kept draining yourself of blood, and wondered why you were dizzy.

Although it isn't as semi-perminant as the blood letting would be (fortunately).
I'm not a Kundalini expert, but from what I have read, it would either just be Chi, or simply a tag name for a concept of spirituality. Meaning saying that when energy hit's X, your enlightened. I would say it would be a mental process in that case rather than a magical energy one. It's just a process with magical titles. Another possibility, to add onto the above, would be it might be using some of the more pure life energy, than what most have normal access to. But I can't see how that would have the effect they are mentioning, but then again, I'm not a kundalini expert.

I do have a good understanding of energy though, so I would say that it isn't just energy alone that accomplishes what that practice says it can.
"Cosmic Energy" from the sounds of it is just some new age term for "powerful energy that isn't you". Ie. they don't know where it comes from, don't care, so "Cosmic Energy" works for them. All energy comes from SOMEWHERE, just most don't bother or care to figuire out where, and in most cases it simply might not matter. I've heard the term, along with "Universal energy". In some cases it's simply ambient energy, or even pulling from a local pool of energy, when it's actually investigated.
I'm asking this because Omni, kinda ecompasses 'everything' and perhaps you need to know about all the energies?
Omni means All. In this context, Omnimancy means All Magic. But more accurately, the name represents the very different and alien to each other techniques and uses of magic that Omnimancy accomplishes and uses. Just like there is biology, psychology, radiology, etc. Different paths of science that have little or nothing to do with each other, however they can be useful to know depending on what your trying to accomplish. It's about versitility. You certainly don't need to know "all energy types" by anymeans to practice omnimancy, you just need to understand what all energy has in common and how to create/use (and sometimes convert) the differences between the types to your advantage. So it's application centric. Research is done all the time to figuire out different applications for what we have, and to figuire out new ways to create other interesting combinations with distinct properties, and their advantages. It sounds more complex than it is.
Just a small second question (I know it is basic, but I heard from a few members that it is better to have a few different oppinions): Sometimes when moving chi/psi around my body I get twitches in the area that the energy is moving, could this be blockage, or just my body firing off nerves that I believe should be being used?
Well, everyone "feels" energy differently. Some as heat, others as weight, etc. If you feel energy by feeling "electricity"/tingle, or even muscle twitches, then it simply might be your body acknowledging there is more energy than normal in a certain place. If there was a "blockage" you wouldn't be able to move it around in that area in the first place. That doesn't mean something isn't "broken", or "scarred" and therefore having a negative reaction to the excess energy. If the twitching isn't painful or disturbs your work, I wouldn't worry about it.
Well, I hope that all answered your questions.
Arthur
-"Its Good to be Da Mage"