Hi. Interesting question.  I have researched poisonous plant listings and can’t find the fuchsia on them.  I then went to the website for the American Fuchsia Society and found information answering you question directly.  They state that fuchsias are not poisonous and that you can eat the berries but they do not recommend eating the leaves.  They go on to say that some are more palatable than others.  Interestingly enough deer also seem to have preferences and will leave some varieties alone while munching down on others.  You can apparently make jam out to of the fuchsia berries. One source called the product bland while another liked it so again, it is apparently a varietal issue or one of personal preference.  I also want to mention that every site that discusses edible flowers talks about the use of pesticides and knowing the source of the flowers that you consume.  One mentions not eating flowers grown in fields where raw manure was used and all discuss the pesticide issue.  Another cautions using flowers collected from a roadside.  Consumption of plants fed with systemic pesticide can accumulate them in the tissues of the plant are not recommended.  Plants sprayed with a pesticide also would be off my culinary listing.

Several online nursery sites were selling edible fuchsias touting the nutritional benefits of the berries but when I searched edible flowers lists I did not find the fuchsia.  Here is a great list of edible flowers from the Extension office of North Carolina State University.  For some reason the link does work  so work you will have to cut and paste it into your browser search box.  Note that it does not list fuchsias.     http://content.ces.ncsu.edu/choosing-and-using-edible-flowers-ag-790  Other places on the internet from non-academic sources list fuchsias and in some cases recipes.  To answer your question about removing the berries from the plant to encourage blooming; yes remove them for a better continued bloom.  Fuchsias are also heavy feeding plants as they grow and continually bloom throughout the season.