Two very separate questions. People frequently use the term conventional mortgage for a variety of meanings, most of them incorrect.
Many people say a conventional mortgage is any loan, secured by real estate that is not insured by FHA or VA. However, most mortgage lenders make further distinctions between conventional loans and other loan types.
For instance, most lenders do not consider Jumbo, sub-prime, or construction loans to be conventional. In fact most of their submission sheets have separate check boxes to differentiate between Conventional FHA, VA, Jumbo, and construction.
So because of all the different opinions, there is no textbook definition any more. It is widely confused with “conforming” mortgage which is a mortgage that conforms to Fannie Mae or Freddie Mac guidelines.
Fannie Mae currently offers a NINA (no-income, no-asset) loan, meaning that technically, NINA can be conventional and conforming.
Conforming is also widely considered to be a loan with at least 20% down, with full income documentation, and not insured by FHA or VA, but this is not the case. Conforming simply means it conforms to Fannie and Freddie guidelines.
As of the publishing of this answer 11/16/07, the conforming loan limit for a single family home is $417,000.