If unmarried people practised abstemise (sp?), there would be no unwanted pregnancies, no STD, no need for abortions, no HIV/AIDS, no guilt complexes,
No, if unmarried people were entirely abstinent, unwanted pregnancies, abortions, and STDs would still occur but only within the married population. Idiots like yourself would then probably forget your previous promises that it would all go away if only your advice were taken, and tell those who did that they just didn't follow well enough, or failed in some other way - generating a positive feedback loop that would produce ever more restrictive rules and accusations of people's failing to follow them causing ever more obsessive policing of them, leading to insane puritan extremism and ultimate social self-destruction. Since your rule is utterly unenforcable (and every obsessively puritan society that has ever attempted to do so has proved this), however, that's not a situation that need even be considered; indeed, I would expect the system to stabilise at the point where the increasing obsessiveness and restrictiveness of the rules is balanced by the increasing inability of your followers to adhere to them or their tendency to disregard them as ridiculous, which is about where we seem to be now.
Whenever you get obsessive belief that a fundamentally flawed premise is failing simply because it's not sufficiently detailed or strong enough, this can only result in positive feedback leading either to self-destruction or, worse, perpetual self-limitation at what is perceived as a non-optimal position by all.
no peodphiles, no little children molested
Paedophilia is unrelated to marital status.
no fornication, and a huge saving in money in health costs and police costs,
Fornication is not, in and of itself, harmful. It is as much a person's reliance on the highly unrealistic ideal of monogamy as naturally virtuous, as is deviation from that restrictive ideal by a partner, that is harmful to a person. It may be theoretically achievable, but the statistics are way against you, especially if you're so prudish that you only date and marry one person in the belief that you both can judge a perfect partner based on the miniscule amount of data thus obtained, given the colossal variety of personalities that will conflict with each other at some point; and decades of marriage are all but guaranteed to find any such incompatible areas and suffer because of them.
As for police costs, if you were to ask the police I'd think you'd find that a very large proportion of their resources are spent on domestic disturbances between married people. This is perfectly understandable; the evolved social characteristics of the vast majority of living creatures tend towards short-term relationships: find a mate, raise young, then leave to find other mates. (I believe the usual span of biological attraction in humans is about 4-5 years - about long enough for a couple of barely-sentient ape-like mammals to raise a child well enough to begin to fend for itself and learn group social rules in a natural wilderness without any artificial structure) This is beneficial in evolutionary terms; spreading your genes among multiple partners increases the odds that some of your offspring will be evolutionarily favoured and reproduce in turn, and minimising the time spent emotionally attached to each one maximises the number of times you can do this in your lifetime. Forcing people, by law, social pressure or religious brainwashing, into remaining monogamous for their entire lifespan goes against this strong evolved instinct and can only increase the likelihood of mental problems and difficulties of living; to maintain a monogamous, intimate relationship any longer than this natural period thus requires more than just short-lived biological attraction, it requires the two personalities to be intimately compatible at every possible intellectual level, and sufficiently strongly capable of "intellectual attraction" to override any subsequent emotional attraction to anyone else, assuming the person believes that emotional and intellectual attraction and attachment should only be to one person at once and at the same time - the average dating period is way too short to guarantee anything like such complete compatibility; it takes the best part of a lifetime to find out for sure if you've really got a partner who's perfectly suited to you, and vice versa.
As for fornication; that's practically a given if you haven't chosen an absolutely perfect partner, and it's only a problem if you're totally brainwashed with the current monogamous ideal anyway; there are, and have been, every possible combination of male and female partners in a marriage or similar relationship throughout human history.
Some have argued that the permanent, monogamous arrangement is common now because it's the one that works best (evolution as applied to sociology; often by people who flatly deny the existence or viability of evolution in a biological context, amusingly); this is a correct, but crucially incomplete answer: it's the best arrangement in the particular social environment that it evolved in. Environments change all the time; human social ones frequently in a decade or less, yet monogamous relationships have been clung to desperately by conservative elements for centuries, and endlessly imprinted on the popular consciousness by saturating our culture; from romantic novels encouraging aspirations to a permanent, monogamous marriage as the ideal (despite endlessly illustrating all the ways it can fail) all the way down to it being the default assumption that bureaucratic forms and social procedures are built around, even now sometimes exclusively.
Can we really be so sure that permanent, monogamous attachment is the best arrangement, suited to modern life in all its other aspects that have utterly changed since such mongamy first became widespread and dogmatically enforced? I think not, and the existence of even a few functional families with a different structure illustrate potential alternatives which at least deserve to be investigated.
