Connecting Android phone with Windows desktop over IP

I am looking for some kind of way to connect android phone with windows computer over internet.I am not sure if this is possible on ,so if other similar solutions are possible you can propose. I need 2 part application. One part will be installed on android phone and second part will be installed on Windows OS on my computer. Part I: App is installed on the phone and after starting need to connect to some Bluetooth buttons (some Bluetooth gadget which I need to buy, I looking to buy two Bluetooth buttons for this ). App just need to have two fields on the phone screen(one for first button and one for second button ) where can be imputed custom text, and update button which when pressed will send that text to second part of application on [login to view URL] start/stop button for app is necessary. Phone screen should be locked on some way when application is active if possible. Part II: App is installed on Windows OS on my computer. She receive signals from app installed on the [login to view URL] have two fields same as on the phone, where text entered on phone fields will be displayed(after pressing update button on the phone). After that two fields I need two square fields (about 50x50 pixels) which will change color when receive signal from phone(Bluetooth button 1 or button 2 pressed). Example: button 1 is pressed --> upper square filed on the computer part of app change color from white to yellow button 2 is pressed --> lower square field on the computer part of app change color from white to yellow App should be adjusted to send as low as possible data across internet(adjusted to low bandwidth(3g/edge) internet) - just sending signal to change color on the square field, and to be as fast as possible. If this is possible, I will draw how this should looks like if this is not understandable. Thanks.