After doing some careful research on the internet:-
White mucus is just an external sign that your Betta is not eating. A lot of sites claim that the white mucus can be an internal parasite (if this was the case) then the white poop will be stringy because then it is actually a worm but this is highly unlikely.
It is more likely that your Betta is constipated, maybe from eating limited foods like pellets. If this is the case then try fasting your Betta for a day or two (don't worry Bettas can live 2 weeks with no food).
Then try feeding your Betta peas (1 or 2 will be enough), remove the shells and microwave them for 30 seconds.
Then try a more varied diet, try feeding your Betta cyclops or bloodworms or daphnia or brine shrimp maybe once a week for a more varied and protein filled diet and the odd pea now and again will help.
Defiantly cycle your tank as Aiken Drum suggested, performing water changes and testing the water parameters.
God blessed them, saying: "Be fertile and multiply; fill the earth and subdue it. Have dominion over the fish of the sea.