Should a non-HMDA bank collect any Government Monitoring information - if they do can they be sited for a violation of that Reg?

All banks must collect GMI under Reg. B for the purchase or refinance of a primary residence, regardless of whether they are HMDA reporters or not.

For a HMDA Bank - if they collect where it is not appropriate it's a violation (overcollecting) - so how can collecting the info be o.k. for a non-HMDA bank?

You are talking about two different regs, HMDA (Reg C) and Reg B, both which have different requirements. (In a nutshell,as a non-HMDA bank you ONLY collect the GMI for Reg B if the loan is for the purchase or refinance of a primary residence. Reg C requires it for home improvements as well as expands it to pretty much all dwellings. So, it's not "overcollecting" for Reg B when you are not a HMDA bank - its required by the Reg. Just be sure it's only for purchase or refi on a PRIMARY. Search GMI in the lending forum and you will see a lot of discussions on this topic that will be of help.