Is it legal for paddlers to land anywhere along the Lake Tahoe shore?

Yes and No.  In California, anywhere below the high water mark is public; however, in Nevada there is no such rule

Can kayaks carry and transmit invasive species?

Yes.  After taking your kayak to another lake, wash and dry the kayak before putting into Lake Tahoe.

What is the history of kayaking in Lake Tahoe?  Who is the first American to circumnavigate Lake Tahoe?

John "Snowshoe" Thompson is the first American to circumnavigate the lake.  For a short history click here.