I. A troubled student and his PhD guide ........... a way for websites to reduce the incidence of spam which troubled internet users in the 2000s.
II. One of the biggest drawback of concrete is that it often develop cracks and scientists have now .......... self-healing concrete.

Here devised, develop and invent mean same thing.
However, usage of 'devised' is most appropriate.
The gramatically correct sentences would read as:
I. A troubled student and his PhD guide devised a way for websites to reduce the incidence of spam which troubled internet users in the 2000s.
II. One of the biggest drawback of concrete is that it often develop cracks and scientists have now devised self-healing concrete.
Option B is correct.