(1) each individual should be rewarded by society in proportion to what he does for society, rather than by his possestions, descent, titles, intelligence, shrewdness, etc.;
That's what capitalism does. If you make a profit, it's because you utilized your capital in a way that society a.k.a. the market values. You get market share by giving customers what they want. You make profits by doing so efficiently.
(2) property and economical rights of the individual are not absolute but are subordinate to the interests of society as a whole,
according to whom? Who gets to decide? Two wolves and a sheep voting on what's for dinner?
(3) the state is supposed to provide public services like health care, education, social security, transportation infrastructure, emergency and security services, etc.;
and the State gets the resources to do this how exactly? By running a bake sale? If a private organization takes things involuntarily, it's robbery. Just because the State calls it "taxation" doesn't mean it's any more moral. You can't delegate the the state the right to take things on your behalf if you don't have the individual right to do that in the first place.
(4) the state should try to ensure equal opportunities to everybody and ensure that everybody has a decent minimal living conditions.
http://www.tnellen.com/cybereng/harrison.html part of protecting consumer rights, socialism implies state intervention when needed to keep markets free, by preventing the formation of monopolies and cartels.
Free markets by definition are free from State interference. Monopolies are only possible with state help. Cartels don't work, witness OPEC.