Short answers, pulled from the story.
A litre is a metric unit of volume equal to one cubic decimetre, the space of a cube measuring 10 centimetres by 10 centimetres by 10 centimetres. It equals 1000 cubic centimetres and 0.001 cubic metres, so one cubic metre contains exactly 1000 litres.
One litre of water has a mass of almost exactly one kilogram, but not precisely. The kilogram was originally defined in 1795 as the mass of one cubic decimetre of water at the temperature of melting ice, yet later redefinitions of the metre and kilogram, plus water's dependence on temperature, pressure, and isotopic makeup, mean the relationship is no longer exact.
The litre has two symbols because lowercase l is easily confused with the digit 1, which in many English-speaking countries is written as a plain vertical stroke. To reduce confusion, the CGPM adopted uppercase L as an alternative symbol in 1979, and NIST recommends uppercase L while the United Kingdom and most of Europe keep lowercase l.
The litre was introduced in France in 1795 as one cubic decimetre. From 1901 to 1964 it was redefined as the volume of one kilogram of pure water at maximum density, but in 1964 the 12th CGPM conference reverted it to exactly one cubic decimetre.
The word litre derives from the litron, an older French unit equal to about 0.82 litres. The litron's name came from Byzantine Greek, where it was a unit of weight rather than volume, passing into French through Late Medieval Latin.
No, the litre is not an SI unit; the SI unit of volume is the cubic metre. The litre is, however, accepted by the CGPM for use with the SI, and the CGPM defines the litre and its acceptable symbols.