whatever I write, I am not a lawyer and we will have to consult e.g., the Free Software Foundation, to clarify these points.
1. Am I legally obligated to provide a software upgrade mechanism on the
device? Do I need to publish the documentation on how to upgrade it?
�6 of LGPL permits combinations of the licensed work or works based on it "to produce a work containing portions of the Library, and [to] distribute that work under terms of your choice, provided that the terms permit modification of the work for the customer�s own use and reverse engineering for debugging such modifications."
So, the *license* of the distributed combined work cannot restrict upgrading / modification of the license part.
As I read that, if there are *technical* reasons prohibiting upgrades (e.g., only signed or no upgrades possible), LGPL poses no restrictions on those.
2. Am I permitted to only allow signed software upgrades?
See above. You cannot forbid unsigned upgrades in the license terms of your product, but LGPL doesn't mention technical means.
3. Many micros have lock bits that prevent further programming without
erasure. Are there any restrictions on setting those?
4. Can I store secrets like private or symmetric keys in flash memory
alongside but that is not part of the flashed binary? This would be
similar to storing those secrets in external EEPROM, which is almost
certainly permitted. This has interesting effects in combination with 3,
including potentially bricking a device if firmware upgrade was
attempted due to erasure of keys.
IMHO the flashed binary can be seen as a file system layout. Part of it might be RIOT, part of it might be your application, and part of it might be some data your application is using.
This data can be put alongside your application, but is not part of it's source code.
It should not make a difference if your application is just opening a file you distribute along with your application, or if it is put somewhere in it's own section by the linker script and your application accesses it using the flash address.
Do you mind if we add your questions to our license FAQ?