Op-Amp power supply and Jitter issue
has a ground reference. But the op-amp does not have one

This is a basic opamp question, and is not particular to your case or your opamp.  Opamps are driven from the difference between the two input signals.  Ideally, the average value of the two inputs doesn't matter.  As long as the inputs are both within the input common mode range, the opamp will function correctly.

Again, this is basic opamp stuff.  Go learn about opamps.

high-speed op-amp (700 MHz unity gain bandwidth)

This is not a good opamp to learn the basics with, which you need to do before getting into advanced topics.  Consider anything over 10 MHz as advanced.  Go get some LM324 and start experimenting.  Put this opamp aside until you have learned how to make the LM324 do a few useful things.

High speed opamps are "twitchy" by nature, and you have to be extra careful in design and layout to make sure all the stability criteria are met.  You're not ready yet to even understand what they are.

What is happening is that the opamp is going unstable during the high parts of the sine.  Are you really sure it is supposed to be stable at unity gain?  Look over the datasheet again carefully.  Try using feedback that results in 5x gain, for example, and see what you get.