will increasing the memory on my mac mini from 2g to 8g make it run faster?

About OS X Memory Management and Usage

Using Activity Monitor to read System Memory & determine how much RAM is used

OS X Mavericks- About Activity Monitor

Understanding top output in the Terminal

The amount of available RAM for applications is the sum of Free RAM and Inactive RAM. This will change as applications are opened and closed or change from active to inactive status. The Swap figure represents an estimate of the total amount of swap space required for VM if used, but does not necessarily indicate the actual size of the existing swap file. If you are really in need of more RAM that would be indicated by how frequently the system uses VM. If you open the Terminal and run the top command at the prompt you will find information reported on Pageins () and Pageouts (). Pageouts () is the important figure. If the value in the parentheses is 0 (zero) then OS X is not making instantaneous use of VM which means you have adequate physical RAM for the system with the applications you have loaded. If the figure in parentheses is running positive and your hard drive is constantly being used (thrashing) then you need more physical RAM.

Adding RAM only makes it possible to run more programs concurrently. It doesn't speed up the computer nor make games run faster. What it can do is prevent the system from having to use disk-based VM when it runs out of RAM because you are trying to run too many applications concurrently or using applications that are extremely RAM dependent. It will improve the performance of applications that run mostly in RAM or when loading programs.

Very very likely yes. The 2010 Mini can accommodate 16 GB of memory

http://eshop.macsales.com/shop/memory/Apple_Mac_mini/DDR3

I would opt for one 8 GB stick and keep one 1 GB stick vice two 4 GB sticks. That way you can upgrade to 16 GB later

Maybe. System slowness can have lots of different causes. Just adding RAM will not necessarily speed up your system.

1. Check your hard drive. The standard hard drive in most 2010 minis was only 320GB, 5400rpm. It's surprisingly easy to fill up that hard drive. A larger hard drive, at 7200rpm will greatly speed up your system.
2. Check your hard drive (again). If your hard drive is more than about 70% full that would explain a lot of slowness. Clean out your hard drive, get it under 50% full and you should see some improvement.
3. Check your appplications. Is your mini slow only when you run certain apps (for example, Photoshop or Final Cut)?
4. Do you keep a lot of apps open at the same time? Close apps you aren't actively using.

There are more possibilities but check these first.

In general, given the increasing demands of newer releases of OS X and apps, it would be a good idea to bump your RAM regardless. At least to 4GB but if you're going upgrade, going to 8GB would probably be a better buy. However, on an old 2010 vintage Core2Duo mini, imho 16GB is overkill.

For what it's worth, last year I upgraded my 2009-era Core2Duo MBP - put in a 750GB, 7200rpm WD Black hard drive + upgraded from 4GB to 8GB RAM ... and it's running like a new machine! Even with Adobe CS6 and Final Cut.