The first one is Sansevieria, common name Mother in law's tongue, and I think the second might be an Aspidistra. The first will tolerate low light conditions, but prefers a brightish spot. Cut off the damaged leaf at the base - it might be that's its been knocked many times as people walk past it, but if its soggy, you may be overwatering. For both plants, water only when the surface of the compost is dry, and only water sparingly in winter. The Aspidistra will need watering liberally from Spring through to Autumn, but again, only when the surface of the compost is dry to the touch. Never leave any water in the outer pot or the roots will become waterlogged, so water, then go back after 30 minutes and empty out any excess water. If there's lots of excess, go back again 30 minutes later and empty it out again. That applies to both plants.
You can repot the Sanseveria in spring if you think it needs it - Aspidistra isn't keen on being repotted, so usually that's only done every 4 years or so, when it really needs it.
Regarding temperature, Aspidistra has the common name of Cast Iron Plant because it puts up with neglect - but it does not like being too wet, and it does not like warm rooms, needs a temperature lower than the average sitting room.

The Aspidistra likes a light place, but no direct sunlight. It will grow in any room. I have one in a warm living room. It flowers every year. I also have one in the bathroom.
They belonged to my Great- Grandmother :o)

You need to wipe the leaves every so often, because they get very dusty.
They don't like root disturbance, so only repot it when absolutely necessary.
Give it a feed every now and then also :o)