Can I connect to Mac Mini Remotely from Mac book?
Yes. You can use OS X's built-in screen sharing. It's a VNC-based application that ships with OS X. You'll need to enable it on your systems in order to use it. Open System Preferences -> Sharing. And make sure 'Screen Sharing' is checked. I recommend the excellent ScreenSharingMenulet -- sits in your menu bar and lists any Bonjour-enabled screen sharing hosts in a drop down when you click on it for automatic discovery and easy connection to shared screens in your network.
Do I need to buy any other hardware for the remote connection or I can do thru Wi-FI available in both Mac MINI and Mac book?
No additional hardware or software is required. You don't even need ScreenSharingMenulet -- you can find and connect to shared screens via Finder if you like.
You do say something confusing your question though:
My aim to have a logical system with 12 GB (8GB with Mac MINI + 4 GB in laptop)for running Virtual Machines on both Mac MINI and Mac Book and be able talk to each other.
You cannot tie the machines together using screen sharing. They won't present themselves as one logical, virtual device to any virtualization software with shared memory or CPUs or any such thing. They will act as completely separate machines, but they can be accessed, graphically, from one another.
If you're trying to tie the machines together to act as a single, unified "super computer" you need to look at much more complicated technologies than anything OS X ships with. Beowulf for clustering and something better than ethernet for inter-machine communication will be necessary like a fiber channel connection (and that will require more hardware).
What about the performance compared to direct and remote connections as it is vital for Virtual Machine communication.
It is difficult to give an answer to this question as it all depends on what you're trying to do when it comes to communication between the machines. On the remote access side of things: over my local wireless network the performance is decent if you use adaptive mode on the screen sharing application but it can get glitchy if you disable adaptive quality scaling. If my macs are all on wires on Gbit ethernet then non-adaptive scaling is quite good. Processes running within VMs on my Macs have good sustained throughput to the Mac's built-in ethernet and wireless network interfaces. Inter-process communication between VMs running on separate Macs is going to be completely dependent on your network and your processes -- impossible to give an answer that'll cover all cases I'm afraid. If you get more specific with what you're trying to do I could possibly answer this more succinctly.