It's been a long time....
It's been a long time since I've flown the 737....and, I flew the -200 (both Basic and Advanced), the -300, and the -400.
As I recall, on the -400, Flaps 1 takeoffs were not certified due to the possibility of tail strike.
I have no knowledge of 737s after the -400, especially the new 'NG' models.
Regarding the use of Flaps 15 for landing, it was (on the aircraft I flew) a legal flap setting for landing. However, my company's SOP called for....
normally....using Flaps 30 for noise and fuel economy reasons. But, under certain conditions, at the captain's discretion, Flaps 40 could be used. Some guys used Flaps 40 almost all the time, as they didn't give a XXXX about saving fuel or making noise. Flaps 15 was reserved for non-normal situations. But, again, it was legal to use Flaps 15 for landing under normal conditions. And, again, some guys liked to do it now and again, just for practice.
It's interesting to note that legal flap settings may be outside your company's SOP. Or, you may not have 'the numbers' for certain flap settings. As an example, Flaps 2 may provide optimal takeoff performance, but you may not have performance charts to validate this.
(Obviously, you have to have the published charts to use any particular flap setting for takeoff....or landing, for that matter.) Flaps 2 may provide the best accelerate/stop performance, and, at the same time, provide the best single-engine climb gradient should you experience an engine failure at V1 or after. But, again, without the charts to prove it, you cannot use it. And, again, on the -400, I'm thinking Flaps 5 was the least flap setting you could use, due to tailstrike issues.
Boeing certifies (through the FAA) many different flap settings for takeoff and landing. You may not know this, as your company does not allow this or that....or does not publish numbers for these settings. For example, on the airplanes I flew, it was a legal flap setting to takeoff with Flaps 25. If I recall, Boeing came up with the certification numbers for this so some operators could use the aircraft in and out of unimproved strips.
Again, I don't know anything about the new 'NG' series. Some of these new 737s are quite long, and tailstrike issues are a concern. This may limit takeoff flaps to Flaps 5 or greater....and landing flaps to Flaps 25 or 30 or greater. (Leaving Flaps 15 landings only for non-normals.) Again, I don't know. As always, you company's SOP is the 'Bible'.
Fly safe,
PantLoad