At the moment, a question puzzling me is why and how glass fibers degrade in water environment? As the degradation of the glass fibers occurs, its reduces the strength of them. As far as I know, the degradation occurs slower in seawater (containing ions) than in distilled water, which in my opinion indicates that process is related to dissociation of glass material.

How does this degradation occur and why is it different for seawater and distilled water? Do I understand correctly, that E-glass is slowly partly dissociating into ions in water environment? Or is it ion-exchange or some other mechanism?

First the how. There are two factors which impact this process which is the dissolution of sodium and the dissolution of silica. The dissolution of sodium occurs first as evidenced by a plot of pH vs time for a glass powder in water and proceed via electrophilic attack: $$\ce{Si-O-Na_{(glass)} + H2O_{(l)} \longrightarrow Si-O-H_{(glass)} + OH-_{(aq)} + Na+_{(aq)} }$$
The second step is the dissolution of the silica which proceeds via nucleophilic attack: $$\ce{(-O-)2Si(-O-H)2_{(glass)} + H2O_{(l)} <-> Si(OH)4_{(aq)} }$$