Disclaimer: I am not a lawyer and this is not legal advice.
GPL is a copyleft license. It means that you legally obliged to distribute derivative work under the same or equivalent license (see here https://en.wikipedia.org/wiki/GNU_General_Public_License#Linking_and_derived_works for instance).
LGPL is a more relaxed license in this regard and allows ...
No, what you propose is not legal.
The LGPL license is written in such a way that the linking exception only works one way.
All the code that an LGPL library depends on must be under a GPL-compatible open-source license
Code that depends on an LGPL library may use a GPL-incompatible license.
The fact that the LGPL library gets used by a GPL application is ...
The problems here are the requirements that "If someone modified this framework it need to be published" and "If someone use this framework for testing - nothing should be done, but it will be nice to know".
We have written elsewhere here about publication requirements, and the fact that such a requirement is considered to make a licence non-free. A free ...
As I understand it, noting that IANAL/IANYL, and assuming that Peter is an employee of his company rather than a contracted resource:
1a. Mostly correct. You also have certain labelling and license-distribution obligations (see eg LGPLv3 s3); but as regards the provision of actual code, I think you're right.
1c. Correct; Peter must either ...