Hi,
I read through your project description very well and I am interested in doing this project for you. About me, I am a professional software developer with more than 5 years experience in developing applications for small and medium sized businesses. I currently run a small tech startup that specializes in mobile, desktop apps and websites. As you can see I don't have any ratings because I recently joined freelance but this doesn't mean that I am incompetence because I can surprise you if you let me do this project.
According to your project, you want a remote control in android with remote screen that sends clicks and strokes. I have done something similar before, I made a remote control in android that controlled a windows PC. The available functionalities were: controlling the mouse pointer in the remote PC, right left and middle click, mouse scroll, keyboard simulator including special keys for windows such as WIN key, keyboard shortcuts etc. the application had more room for customization but I only needed fewer functionalities. This knowledge has really made understand how such systems work and the challenges they face.
The only part I did not understand is whether you want the remote screen to be an android device or not. If so, then you will have to consider rooting issues. If not then indicate what the remote device will be. For any clarifications, contact me via chat. Thanks for reading my proposal and I look forward to work with you in this project.