I have similar processes running on my MacBook and my Mac mini
35 /System/Library/CoreServices/RemoteManagement/AppleVNCServer.bundle/Contents/Su pport/RFBRegisterMDNS
83 /System/Library/CoreServices/RemoteManagement/AppleVNCServer.bundle/Contents/Su pport/VNCPrivilegeProxy
95 /System/Library/CoreServices/RemoteManagement/AppleVNCServer.bundle/Contents/Ma cOS/AppleVNCServer
I'm thinking the RFBRegisterMDNS is responsible for advertising your Screen Sharing server over Bonjour (aka Zeroconf, aka Multicast DNS, aka mDNS).
I'm thinking the VNCPrivilegeProxy is related to the System Preferences -> Sharing -> Screen Sharing -> Computer Settings -> VNC viewers may control screen with password: xxxxxxxxxx. When I do a 'strings' command against the VNCPrivilegedProxy executable it mentions /Library/Preferences/com.apple.VNCSettings.txt, and when I Google that com.apple.VNCSettings.txt, I found references to setting the VNC password.
Basically I think you have the correct processes running, and the RFBRegisterMDNS and VNCPrivilegeProxy processes should only be involved in the initial connection and have nothing to do with displaying the screen.
That leaves AppleVNCServer which as the process responsible for exporting the screen, and most likely the one sending your an empty screen (as I would expect, except that I also expect it to send you a nice copy of you screen and not a blank screen :-) ).
You want to look at the Mac mini console logs.
/var/log/secure.log
/var/log/system.log
/var/log/windowserver.log
for starters. See if there are any VNC related entries. You can also use the Applications -> Utilities -> Console app to look at the logs.
NOTE: When looking at logs, check the time stamps, as you do not want to be looking at old entries. You want to attempt to make a connection from your MacBook Pro to your Mac mini and then check the Mac mini logs, checking the time stamps to make sure VNC related entries, or any entries around the time of your attempt have relevance.
With respect to preferences relevant to the server, these may be what you want to look at and maybe trash (or at least move to see if they change anything)
/Library/Preferences/com.apple.RemoteManagement.plist
/Library/Preferences/com.apple.VNCSettings.txt
/Library/Preferences/com.apple.ARDAgent.plist
If you do move (or delete) these plists, you will need to use System Preferences -> Sharing -> Screen Sharing to enable the relevant Screen Sharing preferences again. Set the minimum needed and then work you way up to move involved settings.
I would also stick with Sharing -> "Screen Sharing", and ignore Sharing -> "Remote Management"