Right now you need to raise your chlorine. With a CYA of 50 your minimum is 4 and your target is 6-8. Letting it go below your minimum is an invitation to algae. You probably need to increase your SWG setting or runtime. I would add liquid chlorine right now to get to my target and not wait for the SWG to catch up
You can add chlorine and stabilizer at the same time, for a SWG your CYA should be 70-80
The only two you have to watch out for is the chlorine and muriatic acid. There two do not play well together. You should have your pump running when add each one. Wait about 15 mins or so between the addition of these two. Other than that it really does not matter as they all work together to give you a balanced pool.