My question is unit 38 is short range weapons only and Deer Flat National Wildlife Refuge Lake Lowell, Unit 38-1b, 38-1xb is all that is closed in unit 38 because it is controlled hunt only?
For general deer season in Unit 38 you can hunt the short-range weapon season and/or the archery only season. Both the Regular Deer Tag and the White-tailed Deer Tag are available to be used in Unit 38; but make sure your tag matches the season and method, and species your are hunting. The Regular Deer Tag can be used to harvest a mule deer or white-tailed deer in Unit 38 in the season for that tag. The White-tailed deer tag is only valid for a white-tailed deer during the season for that tag. There is no any weapon (rifle) season for Unit 38.
You are correct that the Lake Lowell section of the Deer Flat National Wildlife Refuge is closed during the Unit 38 general deer hunts. You can only hunt on the Lake Lowell section of the Deer Flat National Wildlife Refuge if you draw the antlered or antlerless controlled hunt(s) that are available for that area. There are other portions of the Deer Flat National Wildlife Refuge that are not contiguous with the Lake Lowell section that are not part of the controlled hunt but would be part of the regular season hunt.
In addition you should be aware that any State Park in Idaho is closed with a few exceptions. To see these exceptions you can look them up on page 96 (left hand column) of the 2015-2016 Big Game Regulations.
Also remember that most cities/towns have a regulation against discharging a firearm within city/town limits and this usually includes bow/arrows.