The Braun brand cap will fit perfectly, if you still have an old one. Otherwise, there is no real way besides maybe plastic wrap and a rubber band. This is a cost saving measure, to use a foil seal instead of a plastic cap to make the product less expensive. Hopefully in the future we'll have something to better mitigate this issue.
The solution is made from a blend of alcohol (for sterilization), lubricating agent, emulsifier (to combine the water and alcohol), and a lemon scent.
For the quickest disposal, stop up the sink and fill with water, dump the solution into the water, and let it all go down the drain. Then, flush the sink with water for a minute or 2. The dilution of water makes it safe enough to go down the drain. Otherwise, you can leave the open cartridge outside in a place where any animals can't get to it, and let it evaporate.
No. They are not the correct plastic composition for them to be recycled.
