tanivula: It might not 100% solve the issue, especially going through your details, but have you thought of trying a UPS? We've got a HG556a and it's been rock solid ever since we got a UPS, similar line stats, also with snap, and use all the programs you've listed except via wireless - no LAN clients. Main reason I got the UPS was because of VoIP but I think it also filters out a fair bit of the harmonics and cylinder switching stuff the network companies inject into the lines as I can recall we would have daily drop outs around 3 - think due to power line carrier (hot water circuit switching).
Might not solve your problems, but it's worth a shot I reckon, plus you'll end up with a UPS
A UPS would be more expensive that the fritz box wouldn't it?