Temperatures averaging 50°F/10°C - 75°F/23.8°C are ideal but not below 40°F/5°C and avoid frost.
Plenty of sunshine will keep this cacti more than happy. In a glass room you may have to provide some shade during a hot summers day to prevent sunburn.
From spring until fall; water similar to many other house plants by watering when the soil begins drying. Before and during winter barely water the plant. Overwatering, especially when the temperature becomes cold can rot this species.
A pot mixture used for cactus plants that drains well will suffice. Adding gravel or small pebbles at the bottom first few inches of the pot will encourage drainage.
When they are young and growing it's best to re-pot these once a year; during spring in a slightly bigger container. Once they mature re-pot maybe every 2 - 3 years or when necessary.
Feed every 4 weeks with a high potassium fertilizer during summer.
Humidity does not seem to be a major concern for the Echinocactus grusonii, which makes the average indoor environment fine, as it is. Provide as much fresh air as you can , but not cold drafts.
These are propagated with seeds once it fruits after flowering.