How can I count and sum entries per date?

You have to first create a list of unique dates.

If you have dates that are cumulatively ascending by 1 day, then try entering the first date in a new column, say C2, then copy that date down it should increment by 1 day, then you can apply formula.

Or you can select column A, and go to Data|Filter|Advanced Filter and select Unique Values Only, select a location like C2 and click Ok. This should give a unique list of dates, then apply formula to this list...

or you can create a Pivot Table like attached which does all the work for you.