Is it permitted to use a filter on Shabbos. Even if you dont live in the city and there isnt an issue with bugs, can you use the filter to filer out the impurities in the water or is that Borer?

Thank you for your question, it is permitted. The reason is that since people drink the water even without the filter, we therefore don't consider the filter borer. See Shulchan aruch (319;10). However someone who wouldn't drink the water without the filter - see beur halacha הואיל and piskei teshuvot, and shemirat shabbat kehilchata (3; 50). All the best!