Can you cook with distilled vinegar or make salad with distilled vinegar?

Yes. See the attached link.

When you're cooking with vinegar, try using a specialty rather than white vinegar. Apple cider, raspberry, red wine, and other vinegars impart a different taste than white. Good Apple cider vinegar isn't expensive and can be used for both hot and cold dishes. White vinegar is fine but you can make your dish just slightly better by experimenting with the different vinegar varieties available.