You need a real plumber who has the kind of auger that will properly clear the drain. Most DIY snakes are too puny to clear clogs. The usually just punch a hole through without clearing them. Don't waste time or money on chemicals, they not only don't work they will create a hazard for the plumber who ends up doing the job. Your toilet problem may the due to a cheapo builders grade toilet and might not be related to the drain clogging issue.