As you are an excellent English speaker, getting a job once you are in UK is relatively uncomplicated, as long as your immigration status allows you the entry into the country. Before you obtain your social security, you will need to open a bank account (usually during the time when you are looking ...
I do not think him claiming for an amount of time short as such could impact the application for citizenship. If his documentation is arranged in accordance with any paperwork related to his employment as well as the claims, it seems explainable to any official who will handle this.
I would also suggest consulting with a Worker's Law specialist in your area who may point at very concrete details which you want to consider in case you need to present your arguments officialy.
There will be new interviews held at the end of March in case you are still wondering about them. I would advice calling up and finding out the exact times.
