Logitech Touchmouse or PCRemote should do the trick. Both are free, and while PCRemote has adverts it does do a load more than just mouse and keyboard iirc (been a while since I used it, just tend to get up and walk/crawl to the tv ).
local network or when your out and about. I use teamviewer on my mobile devices to control work/home/laptop when I am out and about.
3 options: 1. teamviewer if you want to see the pc screen on your phone while displaying it on a different display 2. Microsoft RDP app, it is smoother than teamviewer but will lock your monitor and requires a pro (or above) version of windows 3. Remote mouse, works like teamviewer but you do not see the screen on your phone instead you have to look at the monitor for it (I use this with display screens in work)
If you run chrome on your desktop, google have made a remote desktop app that you install on your pc and set a PIN, then you run an app on your phone and you can remote control it from anywhere you have an internet connection on your phone, it is really really good. Worth a look into. https://play.google.com/store/apps/details?id=com.google.chromeremotedesktop
only if your network adaptor supports it, might need to turn on wake from lan in bios, can be a pain though if something continually pings your machine, waking it when you'd rather it wasn't.
Yeah, and when you set it up it advises disabling sleep. A brief test today and you can connect when it is at the windows user login page so I guess I'll just need to ask the missus to switch on whichever machine I need to connect to.