How can I actually find out the exact maximum profitlevel of output where profit is maximized?
You could find it by using your table to build a graph and interpolating the quantity that matches the maximum profit.
Note: At this price of 7 Euro your firm should exit the market, as it is under in every point in this table, the minimal loss is -900 either for 100 or 200 units of its product, thus the answer to your question is units = 150.
It will profit if it continues to grow, as its Average Total Cost is decreasing and the firm still benefits from economies of scale.
You could calculate the profitable point by extrapolation.