First about the Frost blade it says that it adds +1 to the user's strength. That means you must use the frost blade for the extra strength.
The Scorpion Chainsword says that it adds +1 strength to the models attacks. If he makes attacks, they are at +1 strength, and don't even try to go on about their guns being at +1 strength because it says attacks, not shots. If a guy has a Scorpion Chainsword his A abilities have +1 strength than normal.
As for pg. 46 paragraph 2. It says only 1 type of special attack can be made. So no you can't combine a force weapon and a powerfist as they are both special attacks, but the Scorpion Chainsword doesn't say that the +1 strength bonus is only for attacks made with the weapon. It just says for the models attacks. If it said "+1 strength to the users attacks", I would agree that you don't get the bonus. If it said "+1 strength to attacks made with it," I would agree that you don't get the bonus, but it just says +1 strength to models attacks. This means that the +1 strength bonus isn't for its own special attack, just the model who is equipped with it's attacks.
As for the powerfist not saying that you only double strength for it. It does specify that. It reads that it doubles the user's strength, ignoring armour saves. Which means you either get both effects (doubling of strength and ignoring armour saves) or you don't get any because again it says that it doubles the users strength, implying that you must use it for the benefit.
I agree this shouldn't give the +1 strength, but it does, and is either intended to do so, or just poor wording. Besides that, the +1 strength makes it a 7 instead of a 6, and really only makes a difference if you are fighting high toughness things like MC or vehicles. Its not like the +1 strength makes them able to kill by double strength because, its an odd number. It's not like its overpowered or anything. These guys cost about as much as a space marine for 1 more Initiative and 1 less strength and toughness. The chainsword makes them worth the points, and really how many of these strength 7 powerfists do you have to go up against anyway?
For 187 points you can have a squad of 10 of these guys with an Exarch and Scorpion's Claw, taking up one of the elites slots. I can have 10 CSM with a champ and a Powerfist for 190 points taking up one of my troops slots. You can have your +1 Initiative, I will take the extra toughness, and I can kill toughness 4 guys instantly with my Powerfist and you can't.
Ya, that strength 7 instead of 6 makes the Exarch such a hardass.....