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Be careful never to let water sit in the rosette as it can cause rot or fungal diseases that will kill the plant.
As with all succulents, careful watering habits and plenty of light will help ensure success.
Keep the plant in part sun to light shade.

With the proper care you should have great success bringing this plant into your home environment. Cactus and succulents thrive in warm weather, so your house temperature should be fine.

Here's an article with tips on how to care for your plant:
https://www.gardeningknowhow.com/ornamental/cacti-succulents/scgen/cacti-succulents-inside-your-home.htm

In short, they need very well draining, dry soil and full sun. For a more detailed outline of their care, this article will help:

https://www.gardeningknowhow.com/ornamental/cacti-succulents/echeveria/caring-for-echeveria-plants.htm

This is, likely, Echeveria agavoides.

This collection of articles will offer more information on Echeverias:

https://www.gardeningknowhow.com/ornamental/cacti-succulents/echeveria

You can remove dead or dying foliage at any time. It will keep your plants looking neat and tidy.

https://www.gardeningknowhow.com/ornamental/cacti-succulents/echeveria/caring-for-echeveria-plants.htm

This is possibly due to consistently wet soil in the cactus container. The damp conditions may be hindering the echeverias' preference for well-draining soil and affecting the cactus, which typically thrives in drier conditions. To address this, consider repotting both plants into separate containers with ample drainage holes and tailored soil compositions. This adjustment, coupled with a revised watering routine, should promote optimal growth and health for both the echeverias and the cactus.

Here are some articles that will help:

https://www.gardeningknowhow.com/ornamental/cacti-succulents