You can track your outbound link clicks in WordPress for free with this plugin. Plugin name; Google Analytics Dashboard for WP (GADWP). Please click to download or search in Add New menu under Plugins page at your WordPress site.

Tutorials is here for how to connect or your other questions

How to Track Outbound Link Clicks in WordPress Tutorial

1. Install and Connect your Google Analytics account to plugin.
2. Click Google Analytics > Tracking Code
   
3. Go to Events Tracking Menu
4. Set track affiliate links to on position and others whatever you want.
5. Set your Affiliate Regex like this: /out/ and save changes. (Generally this auto detected by plugin)
   
6. After that you can login to your Google Analytics dashboard and click on Behavior » Events » Overview page.
   
7. Click Event Label
   
8. For Realtime Track click on Real-Time » Events » page.
9. 
10. Click to “affiliates” under Event Category to see your clicked Outboud links in Real-time