Probably not. Well, it depends. Actually, it's hard to say
riverkee said:
I am going to ask some questions based on my curiosity and my complete lack of knowledge and understanding of the Universe. My biggest hope is those answering can be understanding and patient, and not see it as an opportunity to to be arrogant.
You sound a bit defensive--- I hope that is not based upon experience at PF (I see this is your first post here, at least under the handle "riverkee")!
Information about what books you've read would be more useful than a disclaimer of all knowledge. I'll try to take a stab at your questions on the assumption that you've read some popular science books, but please do not mistake my attempts to informally convey some sense of numerous subtle issues for "arrogance". Your questions appear to involve many difficult points which cannot be truly explained without considerable mathematical machinery and prior mastery of much background material. I'm trying to answer as best I can without saying anything which is terribly misleading.
(Yah, now
I sound defensive!

)
riverkee said:
Are wormholes still a possible theory of what lies at the end of black holes?
It depends upon what you mean by "wormhole".
1. The hypothetical objects known as "stable wormholes", which would maintain long-lived "shortcuts" to distant locations , have never risen beyond the level of a theoretical speculation not supported by convincing evidence, in fact a speculation which many (but not all) physicists regard as theoretically dubious for a variety of reasons.
2. The first "wormhole" discussed in theoretical physics was the so-called "Einstein-Rosen bridge", an old name for what is now called the "throat" of the "maximal analytic extension of the Schwarzschild vacuum", a spacetime used to model a highly idealized nonrotating black hole, nowadays often called the "eternal Schwarzschild vacuum" model. It turns out that while in this model the throat does in some sense connect two universes, it pinches off too rapidly for an astronaut to get through. More important, this "eternal" model is physically implausible; more reasonable models of nonrotating black holes depict black holes formed by gravitational collapse of a star, e.g. the "Oppenheimer-Snyder model". These models have a different "conformal structure" once one passes through the event horizon; their internal structure does not feature throats.
3. Similarly, the most idealized models of charged black holes ("eternal Reissner-Nordstrom electrovacuum"), uncharged but rotating black holes ("eternal Kerr vacuum", and rotating charged holes ("eternal Kerr-Newman electrovacuum") have throats, but in theory the throats in "eternal Kerr-Newman electrovacuum" would
not pinch off. However, it turns out that once again these models are not plausible once when passes through the even horizon. More realistic models are believed not to have throats, although it seems they might feature a "weak null singularity" in addition to a "strong spacelike singularity", and it is possible that objects which fall into a real hole and which miss the strong singularity might pass through the weak singularity unharmed. Unfortunately, gtr itself declares its inabilty to predict what might happen after that! Before you ask, it is not clear that any of the speculative theories being discussed in connection with quantum gravity would resolve the question, although there appears to be room for hope that this might happen should a successful theory of quantum gravity ever appear.
riverkee said:
If so, would that matter sucked into the black holes be scattered throughout our own universe
No. At least, I think that is the best short answer based upon what we currently know about gtr.
There is a long-standing but so far untested prediction by Hawking which is goes outside the domain of gtr into quantum field theory, namely "Hawking radiation", which has led to the suggestion that black holes might very slowly "evaporate". There is controversy over what kind of "stuff" would "come out" in this process, but I think the best short answer is that this wouldn't be very much like restributing matter within our own universe.
The prediction of Hawking radiation is thought to be valid, but it is based upon a tricky approximation and it has not yet been directly supported by experiment or by observation. However, it is consistent with a body of notions called "black hole mechanics" which makes sense in the context of gtr, and has been more rigorously established. According to this, gravitation theories such as gtr should share some "thermodynamical" characteristics, and the most important characterization of a "black hole" should be "thermodynamical". An interesting program being pursued by several groups around the world seeks to lay the groundwork for "analogue black holes" which might one day result in a direct test of the prediction of Hawking radiation (and a Nobel Prize).
The issue of black evaporation (and the related information paradox) is far trickier than the prediction of Hawking radiation and IMO must still be regarded with caution. However, again, analog black holes might one day allow a direct test (another Nobel Prize).
riverkee said:
Classically: perhaps, depending upon what gtr proves to say about the internal structure of realistic black hole models. This would then raise some philosophical difficulties about how one might test this even in principle (after falling through an event horizon, how would an intrepid explorer report his findings should he survive?)
In quantum gravity? Who knows? I think the safest brief characterization is that very little is yet known with confidence about what a successful theory of quantum gravity might look like, despite a great deal of work, in part because the theories so far explored are quite challenging, and in part because there is almost no clear experimental or observational evidence to guide theorists.
riverkee said:
Could the matter from a galaxy billions of light years away, whose light we only see now, and has long disappeared, been the makings for own solar system or galaxy?
Via vanishing into black holes? And reappearing after a few billion years? I think the best short answer is almost certainly not. In particular, evaporation times for stellar mass black holes (if black holes do indeed evaporate) would be much longer than that!
riverkee said:
If this is so, is it possible the total matter in the Universe, as we see it, is slightly less than perceived as it sort of recycles from one point in Universe to another leaving only light ahead of it's present?
You might be asking about "pre-Big Bang cosmology", another speculation which has been kicked about for some time. That depends upon yet another set of ideas, including Penrose's "Weyl curvature hypothesis" and "dark energy".
There is a notion of supernovae blowing out stellar material, which forms dust clouds and may be later recycled to make new stars, but this recycled matter would certainly not have been "inside" a black hole, not even if the collapsing core of the supernova forms a hole.
OK, your questions were pretty vague, so I think that's the best I can do towards vaguely (non)-answering them.
Further reading, at the graduate level, for ambitious inquirers:
http://relativity.livingreviews.org/Articles/lrr-2006-3/index.html (review of tests of competing gravitation theories, e.g. gtr, Brans-Dicke)
http://relativity.livingreviews.org/Articles/lrr-2007-4/index.html (review of some of the available evidence bearing on cosmology, specifically that bearing on determination of cosmological distances and expansion rates)
http://www.arxiv.org/abs/gr-qc/0604102 (review of exact solutions of the EFE, including some discussion of the global structure of Kerr vacuum etc.)
http://relativity.livingreviews.org/Articles/lrr-2004-1/index.html (reviews conformal structure, although mostly focused on the regions very far away from black hole models, rather than "deep inside" them!)
http://relativity.livingreviews.org/Articles/lrr-2005-12/index.html (review of analog gravity)
http://www.arxiv.org/abs/0710.4474 (reviews speculations about hypothetical "traversable wormholes", hypothetical "time machines", and hypothetical "warp drives"; beware the authors abuse of terminology "solution"; according to him, any Lorentzian manifold is a solution of the EFE, which is dangerously close to claiming that gravitation theories are "vacuous by design")
http://www.arxiv.org/abs/0710.4919 (one flavor of speculation about hypothetical "pre-Big-Bang" epochs)
http://www.arxiv.org/abs/0710.2696 (speculation about hypothetical creation of traversable wormholes in the LHC)