Need to have the keyboard and mouse 100 feet away from Mac

That is an N wifi repeater, not a BT repeater. You searched using BT as a search term and that is why it shows up in the URL.

http://www.newegg.com/Product/Product.aspx?Item=9SIA5YF1ZE5515&cm_re=bluetooth_e xtender_booster_repeater-_-9SIA5YF1ZE5515-_-Product

KFLY- Newest US Plug version V1.3 300Mbps Wireless WiFi Repeater with WPS Function 802.11N Network Router Range Expander Booster Complies with IEEE 802.11N/G/B

If yo have wifi everywhere, use a laptop and screen sharing but do not use the screen. You can also use an iPad with suitable apps.

In your case with the need to control it from multiple locations the best and realistically only solution is to use Screen Sharing to remotely control the Mac.

With this solution you can control it from anywhere you have a network connection and could use a laptop to control the Mac mini. This is the solution I use in a very similar situation.

Bluetooth does not have enough range, even RF wireless keyboard and mice devices also would not have the range, and I don't believe there is a suitable USB solution.

The only other possibility that occurs to me is to use an IP based KVM. A KVM (Keyboard/Video/Mouse) switch box allows multiple computers to be controlled from typically a single keyboard and mouse. However there are versions which allows you to do this over a TCP/IP network i.e. Ethernet. Then again you would be able to do this anywhere on your network. Here is one example - http://www.aten-usa.com/products/productItem.php?model_no=CN8600

Personally I still strongly recommend using Screen Sharing. Its built-in and completely free!

Where is the monitor?

Bluetooth with a range of 1 to 10 m is not a viable option.

You could try something like a USB extension/extender like:http://www.cablestogo.com/category/usb/usb-extenders-extensions that says it has a range of 100 m.