Mavericks Bluetooth : Connections from undesirable (unpaired) devices... Where is the Advanced Bluetooth option? My problem :

Recently I started to use a Magic Trackpad for my MacBook Air (Mid 12), and discovered some annoyance :

I regularly see some devices connected to my Mac by Bluetooth, the one that I never paired...

One of this devices is my FitBit One, which is not paired to my Mac, but still can connect and use it's (fitbit) battery...

Some others devices appear from time to time with different names, that I do not recognise... Sometimes I know when another device, that my Trackpad, is connected because the trackpad starts to freeze.

I tried to "remove" an unwanted device, but it keeps reappearing...

I can't even imagine what I can do, since the bluetooth options are really limited...

Question :

Is there some way to have an advanced bluetooth options? So I could "force" all devices to ask a permission before even trying to connect to my Mac?

I found some screenshots of advanced view here :  Securing Bluetooth

But this is an old one and I am afraid that in Mavericks the only "advanced option" is limited to "alt + bluetooth" which gives nothing useful to me.

If anyone have an idea how to fix this problem (but still keep using my trackpad :) ), it would be great to share with me :)

Thank you in advance!

EDIT (29/08/14)

Some precisions : I detected this problem by seeing my FitBit One battery life going from one week to 48 hours, exactly from the moment I started to use BT on my Mac. 
I use my Magic Trackpad only at work, and I already checked, if I leave my Mac working all night my FitBit will loose somme battery life in one night, and my Mac is the only device with BT enabled...

Here the link where you can see my One listed as Connected, but I never paired it or was asked to. Link
When you say that you see devices connected to your Mac, are you in the Bluetooth Preference Panel or are they appearing in a different app?

Normally your BT is not in discoverable mode, meaning other devices can't see/pair with it unless it has already been paired.  When you open up the BT Pref Pane, the discoverable mode is automatically switched on.  When this happens, it will list all of the available BT devices it can find (like your FitBit) so that you may pair with it.

If it isn't already on, in the BT Pref Pane, enable the "Show BlueTooth in menu bar" checkbox.  This will add the BT menu in the right side of the menu bar.  Clicking on this will show you the currently paired devices and other basic functions.  However, if you hold down the Option key then click on the menu, you are shown an advanced menu. This will show you if your BT is in discoverable mode or not, which it should only be on if the BT Pref Pane is open.

If there are any devices listed in the menu that you don't want paired, choose that device's submenu and select Remove.