1) Shiloh, 1st Minnesota Battery, flag was captured "Silk Battle-Flag, with gilt crossed cannons and it was captured in their camp, near General Prentiss's Head Quarters". It is unknown what CSA regiment captured the flag. Source: http://books.google.com/books?id=wJvlAAAAMAAJ&pg=PA208&dq=1st+Minnesota+Battery+flag,+Shiloh&hl=en&ei=bJJ1TsizLe_IsQKw0NSLBQ&sa=X&oi=book_result&ct=result&resnum=10&ved=0CF8Q6AEwCQ#v=onepage&q=1st%20Minnesota%20Battery%20flag%2C%20Shiloh&f=false (If that link does not work, "Confederate Veteran, Volume 22, Issue 5, Page 209.)
2) I question the 1st Minn Infantry at Jerusalem Road, June 22nd, 1864. They were a two company "Battalion" and certainly were hit hard and just to the right of Captain McKnight's 12th New York Battery which lost four pieces.
I will have to dig around on more Minnesota regiments, many of them fought Indians and not in the actual Civil War.
Have a good morning,
Shawn Prouty