Can I donate my body to science and some of my organs to someone else?

Yes. Yes you can. You have sign up to be a donor and specifically tell your family members about your wished.
Yes. At times the deceased patient in a will or instructions given to the next of kin may want to restrict the types of organs that are removed for transplant. However, this decision must be made promptly at the time of death in order for any organs to be useable for transplant.
Must state priority. The circumstances leading to death will determine whether or not organs or tissues can support lives through txp. If that is your priority, they need to be treated very specifically. If instead, priority is use of the body for science (such as med students learning anatomy), txp may not still be possible. Complex issues. Best to discuss preferences with family. Thank you for the generous thoughts.