Water going out badly from sinks and shower - how to locate the issue?
I would get a small bucket, put it under the trap for the slow sink. remove the trap, check flush, and clean out the trap. After you reinstall this trap see if the problem is corrected. If cleaning out the trap doesn't fix the drain check the piping between the trap and the vertical larger stack. If the drain problem is not fixed either buy or rent a snake to snake the drain or call a plumber for help. Where I live plumbers will come out for around $100.00. (money well spent)