Does one liter equal one kilogram?

Answer 1

The density of water changes slightly with temperature and water has its highest density at four degrees Celsius. At this temperature, one litre of water weighs one kilogram. At other temperatures one litre will weigh slightly less, but 1kg is still close enough an approximation.

Short answer: For water, yes. For anything other than water the mass would vary depending on the density of the substance.

Answer 2

Depends on the substance. For water it does, for air it doesn't.

Answer 3

No, 1 liter of water is but oil is lighter than water (also partially why it floats on water). Oil has different densities depending on type so your question isn't specific enough to answer.