I have a 3-speed internal gear hub. After switching between gears no pedaling is possible until I rotate the chainring about a half turn. Is it normal or did something go out of adjustment?
That is a sign of the gears getting out of alignment due either to the cable stretch or the rear wheel axle sliding back from the drop out. That pause will become longer as the misalignment gets worse. If you have a Sturmey-Archer hub, you can tighten the axle indicator by half a turn. This is a derailleur system equivalent of a chain sitting halfway between rear cogs and a barrel adjuster used to compensate for it.