Firstly, I would point out that the websites you linked to seem fairly antagonistic towards the mainstream of astronomy. While not in and of itself a disqualifying property, it does get things off to a bad start. One particular statement that I have to point out is wrong about astrophysicists is from your third link, under the heading "Chapter 1", the seventh paragraph of the section "Questions and Answers" which says, "Astrophysicists do not study experimental plasma research in graduate school. They rarely take any courses that discuss Maxwell’s equations and electromagnetic field theory." As a first year graduate student heading towards working in astrophysics and cosmology, I can attest heartily and strongly that at least the second sentence is patently untrue (as I have an exam on advanced electromagnetism this coming Monday... :) ). Again, not disqualifying, but
Secondly, there's a lot of exposition, but not a lot of numbers/equations. Maybe it's that these are intended for a popular audience, but it may be a more general issue. Moreover, whenever I read things that claim to have discovered something radically new and different from the mainstream, when they do give numbers, they usually eschew mentioning estimated errors (go to http://xxx.arxiv.org/list/astro-ph/new and pick a paper at random, and look for numbers... they should have a "+/-" such and such to represent an error. I'd beware ones that don't give an error estimate). They often times presnt results without giving reasoning.
Thirdly, mainstream cosmology is dismissed as too theoretical while plasma cosmology explains observations as they exist. The issue here is that there is some value in having an explanation which is a bit ahead of observations as it gives observers something specific to look for which can help prove or disprove the said theory. So a theory which sticks its head out a little bit is desirable. One which sticks its head out too much is probably just asking for trouble, admittedly.
Fourthly, reading some of what is on Arp's website (he's spoken of highly in the second link, as the "Galileo of the 20th Century"), it seems somewhat silly. Under http://www.haltonarp.com/articles, the article "Faint Quasars Give Conclusive Evidence for Non-Velocity Redshifts", apart from being devoid of any equations or numbers of basically any kind (see point number two), his argument seems to be that among several objects obersved in a survey of the sky were close together, including two of high redshift (quasars) and two of one of low redshift and that this is somehow evidence that quasars are high redshift ejecta of low redshift objects (where high redshift is generally taken [in mainstream cosmology] to mean greater distance, though I don't remember what Arp thinks). He furthermore says (with no math or citations in support) that the odds of this being a chance alignment (which would be the mainstream explanation) is 3.5 chances in 10 million (or, about one in three million). Granted that the survey (according to Arp) only catalogued 243 objects, still in astronomical terms those aren't bad odds. Moreover, one is tempted to ask why, if this is something we should expect, don't we see it *more* often? Why was there apparently only an alignment of these three objects out of all the 243 catalogued in that survey? Wouldn't one think that there should be stronger relationships? Of course, without a firmer (and preferably somewhat mathematical) explanation of any expected relationship, I have little to say.
Fifth, as to the explanation that stars are nexuses of galactic currents, this it seems to me would be readily testable, even with data that we should already have. After all, let's say you have two lines of current crossing each other at the position of the Sun. Wouldn't a space probe, while travelling around the Sun (or even the Earth) pass through varying electric and magnetic fields, something which is potentially readily detactable? And we have been sending out lots of probes across the Solar System, so that we haven't heard of such things from all that travelling seems disappointing, though admittedly it's not conclusive. And again, without knowing the mathematical details, I can't say anything more concrete, though I would ask the question, "Where is the energy which these currents are pumping into stars coming from? Or if it's always been around, where did it come from, or how did it assume the observed form over possible alternative forms?" If the answer violates the principle of conservation of energy, then all bets are off and we can't say anything about the rest of the universe (after all, if the laws of physics as we know them on Earth don't apply across space, whatever's happening in the universe might as well be magic for what we know; this of course, isn't ruled out by mainstream cosmology, but it's the only reasonable assumption to make, as without that we have nothing to base any astrophysics of any kind on...). These are questions that are asked in mainstream cosmology and theoretical physics.
I think I'll stop there before my fingers fall off. I could spend more time, but I have other things to do (remember that exam... :) ). To make a long story short, these theories do seem to be pseudo-scientific and not very rigorous. That's not to say mainstream cosmology should be treated as sacred: it's just the best set of answers we have so far. There are problems (not leastwise, what are Dark Matter and Dark Energy), problems which could potentially lead to answers which would flip cosmology on its head (the "discovery" of Dark Energy being an example; we really don't know what it is, or why it's there, and we certainly didn't think ten or twelve years ago that it would be there...).