Eye diagram measurement of a CLK using an Oscilliscope
Eye diagrams are not really useful when looking at a clock signal because to make any sense of it requires triggering on the rising or falling edge. Once that is accomplished it won't look like an eye diagram: -



It will look like this: -



Now, to my mind, that is not an eye diagram.


  My second question: Is the eye diagrams just using to measure CLKs, or
  one may also measure Data using eye diagram?


Not useful for clocks because they are technically not eye diagrams BUT very useful for continuous synchronous data. If the data is asynchronous and sent in short burts then it's not useful because the eye diagram will "fail" in between burts. If looking at asynchronous data then use a storage scope and capture several bytes and examine as if examining the clock signal mentioned earlier. Maybe like this: -