If these are old toilets, then they can use a rebuilding like everything else that wears out. Replace the ballcock assembly and put in a new flapper. The fluidmaster ones are highly regarded by plumbers. A bad and waterlogged flapper could be the cause you have to hold the one handle up for 7 seconds.
The lack of the spiral effect could be the holes under the rim and and one at the bottom are plugged. Get a coat hanger and start cleaning them out. A light acid like limeaway will help get some of the built up crud off. There could be a partial plug downstream for it or could be something in the bowl trap which would require removing the toilet, turning it upside down, and removing the stuck object(such as a toothbrush). Removing the toilet will allow you to inspect the floor for water damage and then put in a new wax ring so you don't have to worry for years to come. Get new brass bolts at the same time.
Last thing you want to do is buy the new 1.5 gallon flush toilets if you can help it.