For the former, yes, there are certainly pieces of art by Hitler around. Several have sold in recent years, including:

Standesamt und Altes Rathaus Muenchen (Civil Registry Office and Old Town Hall of Munich),plus associated documents, sold in 2014 for €130,000.

Maritime Nocturno sold in 2012 for $12,000

In 2009, a collection of 14 works by Hitler sold for over 98,000 GBP (http://uk.reuters.com/article/2009/04/24/us-hitler-idUKTRE53N2M620090424)

You can see some of his surviving works on artwiki: http://www.wikiart.org/en/adolf-hitler

A previous AskHistorians thread suggests he did not paint while he was in power: http://www.reddit.com/r/AskHistorians/comments/1jg9vz/did_hitler_paint_while_he_was_in_power/