I think that, because the manufacturers define the mpn, it would be OK for them to use their SKU as the mpn. If you are using the same SKUs for your products then it would therefore be fine for you to use them as your mpn.
But I don't see how you could use them as a GTIN - unless it is the case the number that your manufacturer uses for the SKU actually is the GTIN. You cannot simply make up a GTIN whether you are a manufacturer or vendor, they have to be purchased from a body that can issue them, because they are used to classify the products they have to follow a strict numbering system and be unique. In the UK you get them here:
www.gs1uk.org/Pages/default.aspx
Really your manufacturer should already have done this, they are the ones that ought to be able to help you with this. They should know whether their SKU corresponds to a mpn, or a GTIN (also known as EAN or UPC). If the person you have been in contact with does not know this try to find someone who does know the answer. There must be someone within their business who does know the answer. It is possible that they don't know what a GTIN is, perhaps if you explain that they would probably know it as an EAN or barcode number they might understand.
So that the packs are handled correctly, yes you do put the 'Use Identifier exists tag as YES'