I just realized that I did not answer two of your questions.
You are out of luck with the methylphenidate you take. There is no way to dissolve it and have it be stable for more than a day or so. Since the IR tablets only come in 20 mg sizes, there is no way to save a bit of money.
There is no way that I or the pharmacist I consulted know to remove lactose from a solution without adding toxic solvents or heating it to the point that the methylphenidate is destroyed. Sorry, I can’t help you on the lactose problem.