At my previous employer (a top 10 website), I wrote all of the tracking libraries for our various sites. We were VERY interested in tracking pauses, scrolling, swipes on mobile pages, clicks, video pauses, video jogging, switching to another tab, facebook status (logged in, etc.) and much more. A lot of these metrics are important for understanding user engagement and determining what point users are bouncing. We were never worried about the number of server calls being made, and most of these events can be sent in bulk with one request. We used Google Analytics heavily (among others), if you are interested in incorporating some tracking into your software, it is quick and easy to get started with GA. If you are wanting more information as to how to track some of these metrics, I'd be happy to explain.
Tracking eye movement is an interesting endeavor and there are a few solutions out there for behavioral testing/tracking which a quick Google will help you find. The one I'm familiar with is SMI. SMI uses special glasses that record eye movement and fixation and provide a heat map on top of your webpage/app/etc. for analysis, similar to the reports clickheat generates
If just tracking clicks is enough for you, ClickDensity starts at $5 a month for one site, or $20 a month for 10 sites. I'm pretty sure you can afford that.
Alternatively, a free, open source script for heatmaps is ClickHeat. Implementing it the right way will cost you far more in time than the alternatives cost you in money, though.
If you have hundreds or thousands of sites you need to track, here's how you can do it:
Set up a separate hosting account/domain just for tracking clicks.
Make clicks asynchronously load a tiny file on that domain, using domain, page and coordinate data as GET request variables. For example:
http://www.example.com/1px.png?dom=site.com&page=about.html&x=200&y=100
Parse the server logs to get your needed data.
A solution like that will take some work, but it should be cheap and offer decent performance.
If you want to record all mouse movements instead of just clicks, and also want to be able to replay them completely, you're looking at a rather more elaborate problem. I can think of some ways to approach such a problem, but if you have the necessary skills to implement something like that, so can you.
Google Analytics and Click Heat are free and I find them quite useful. Moz (formerly SEOMoz) is also great for fixing a million little errors and dead ends that you never realized your site had.