Below are some links with extensive info on each supplement, from the Linus Pauling Micronutrient Research Center:
You'll be able to identify potential interactions between supplements by looking at each page's Nutrient Interactions section.
As mentioned in the zinc link, from the Adverse Effects section:
"The major consequence of long-term consumption of excessive zinc is copper deficiency. Total zinc intakes of 60 mg/day (50 mg supplemental and 10 mg dietary zinc) have been found to result in signs of copper deficiency. In order to prevent copper deficiency, the U.S. Food and Nutrition Board set the tolerable upper level of intake (UL) for adults at 40 mg/day, including dietary and supplemental zinc."