The product "GC Tooth Mousse" is often recommended by dentists in some
countries - but it's hard to find any objective information about it. Is it
really effective? Does it really remineralize the tooth enamel with
phosphate and calcium ions?

I've found some information like this:
"CPP-ACP Current Research and Clinical Application
Dr David Manton, University of Melbourne, Australia
Casein phosphopeptide - amorphous calcium phosphate (CPP-ACP, Recaldent) is
a casein derived peptide, with added calcium and phosphate, which acts as a
calcium and phosphate reservoir when incorporated into dental plaque and on
the tooth surface. The CPP-ACP nano-complexes release calcium and phosphate
ions via a pH or concentration gradient mechanism to maintain a
supersaturated environment with respect to hydroxyapatite, therefore
reducing demineralization and enhancing remineralization. The ability of
CPP-ACP to remineralise white spot lesions of enamel (WSL) both in vitro
and in situ has been widely reported. Recently, CPP-ACP in sugar-free gum
has been shown to significantly slow the progression and promote the
regression of caries in a randomized, controlled clinical trial. The
addition of low concentrations (<1.0%) of CPP-ACP to acidic sports drink
has been shown to reduce erosive potential without significantly altering
taste. The inclusion of fluoride into CPP-ACP (as CPP-ACFP) forms a novel
material with fluoride incorporated into the nano-complex. Advantages of
increased remineralization are indicated for CPP-ACFP over CPP-ACP due to
the availability of the fluoride ion with calcium and phosphate ions at the
enamel surface, increasing fluorapatite formation".