Resave it in Illy as AI and place that.
Let's say I have many EPS files. Is there a quick way to convert them all to AI with one click?
You can create an Action in Illy.
I managed to convert them all by using an Action in Illustrator.
Is there a way/script to rename all the links in my InDesign document at once, so I don't have to replace them all manually?
Link1.eps would be Link1.ai
Link2.eps would be Link2.ai
...and so on.
Link panel menu > Replace links with extension…