I think daily contacts are safer and cleaner than monthly contacts ,but more expensive . Generally it has little to do with the lazy eyes . if you are not sure what kind of contacts you should wear ,why not call your doctor and seek for the suggestion ?
As I know that color contact lenses can not help with your amblyopia but prosthetic contact lense. If you just would like to enhance your eye color with color contact lenses, then of course it is ok. The daily contacts are safe, hygeian and convenient.However, if you want to improve your amblyopia, I highly suggest you to try prosthetic contact lenses.
Yes, you can wear the daily contact lenses. In my opinion, the daily contact lenses are more safe and effective than the monthly contact lenses because the hygiene is proved. And the monthly contact lenses need the protection, such as the rubbing after the day of use and the soap in the solution and so on.