Percent concentration of 500 μM of H2O2
I will assume you are asking for percent mass/volume, $\mathrm{g/ml}$, since to calculate percent mass/mass you need the density of the liquid (unless you assume it is water which is $1~\mathrm{g/ml}$ so will give the same answer).

We have $500~\mu\mathrm{M}$ of hydrogen peroxide, which means we have $500~\mu\mathrm{mol}$ of hydrogen peroxide per 1 litre of solution. $500~\mu\mathrm{mol} = 0.0005~\mathrm{mol}$. Now you can work out the molar mass of hydrogen peroxide and multiply it by the number of moles to get the mass of hydrogen peroxide per litre of solution. This gives $0.017~\mathrm{g}$. There are $1000~\mathrm{ml}$ in 1 litre. So you have $0.017~\mathrm{g}/1000~\mathrm{ml} = 0.000017 = 0.0017\%$.

For your question about whether hydrogen peroxide is toxic to the eyes, you can search the internet for the Materials Safety Data Sheet (MSDS) of hydrogen peroxide (Sigma-Aldrich is a good site to search). This contains all the hazards associated with this chemical, and when you do laboratory work you always have to look these up for each chemical before you start a reaction. The MSDS states that hydrogen peroxide can cause severe eye damage, among other hazards.