I recently started to build credit, I applied for a CapitalOne card and got approved, about a month earlier I saw the option for Bill-me-Later on eBay, so I had checked if I was eligible, but I wasn't. Besides that there was 1 other hard inquiry on my credit and I don't remember what it was for. As of now I don't have any credit since I just got my first card, but will those 3 inquiries drag it down much?
Inquiries for credit are a small factor in your credit score. They'll disappear from your credit report after two years, at which point they'll no longer have an impact.
Credit Karma has some tools that you can use to see how hard inquiries impact your score, but there's no one true answer as there are many different formulas for calculating a credit score.
If you're building credit, focus on keeping your first card's bills paid on time. That is of far greater importance.