Dear Rabbi, Is there a problem of saying a bracha/davening next to a bathroom? If one needs to do this, is it better for the door to be closed?

ב"ה Shalom To simplify things the best thing would be for the door to be closed. This way there is clearly a partition between the toilet, which is understandably "a place of filth", and the rest of the house which allows you to daven and say Brachot. Explanation and sources: There are many poskim which hold that although our toilets today are immediately cleaned by flushing and nothing remains in the toilet it is still best not to even do netilat yadyim in a room with a toilet. However, when circumstances require it may be done. For summary of opinions see Yalkut Yoseph, Hashkamat Haboker 4: 84-85. Also, in the Hebrew counterpart of this website, Hagaon Harav Dov Lior cites the Chazon Ish among those who are lenient in regard to toilets today when one wants to do netilat Yadayim. All the best and Shannah Tovoh