Tools
Use long forceps or tongs, a spare catch cup and plain water for the dish. Avoid household sprays, scented cleaners and residues inside an occupied enclosure.
Mould
Remove a small local patch with the affected substrate and correct the moisture/ventilation cause. Repeated widespread mould needs a bigger substrate and airflow review.
Full teardown
A full substrate change is for contamination, serious pest problems, persistent foul substrate or a planned rehouse—not routine weekly or monthly cleaning.
Work around the spider
Know where the spider is before opening the enclosure. If it is blocking safe access, close the enclosure and return later instead of forcing the job.