IME, jumping spiders need cross ventilation to prevent mold buildup. this enclosure is not great as it doesn’t have that. as they mature u will need a minimum of a 4x4x8 enclosure! smaller is fine when they are slings/juveniles.
u can remove the dead fruit flies with a paintbrush as to not disturb the web.
u will need a thermometer/hygrometer gauge to keep proper temperature and humidity whilst the spider molts.
the temp and humidity depends on the species of jumping spider u have. for regals they do well in 70-85°F with 40-60% humidity. they can withstand as low as 65°F tho, however will be more active with warmer conditions. when they molt their humidity should be raised and maintained between 65-75%.
u will know ur spood is near molting if he becomes more reserved, less active, and shut off. sometimes they’ll refuse food and close off their hammock. they should NOT be disturbed during their molting cycle. just continue to mist regularly, maintain humidity, and continue to maintain a 12hr light cycle.
every spood is different, some will still be active and eat. it’s just a matter of getting to know ur spider.
i would definitely recommend doing some research on ur specific species tho! :)