Gap in Tax payments

Hi,

I will be applying for Naturalisation under the ILR + 1 year residence rule. I received my ILR on April 2013.

1) I have one motoring conviction which happened Feb 2012. (Speeding 3 points). Will this cause any issue when applying for the
naturalisation. I did mention this offence when I applied for ILR back in 2013.

2) I have few years of work where I worked part time - cash in hand as i was under the student visa. I received my ILR on April 2013 by satisfying the 2 years spouse visa( 2011-2013)
I did work part time and paid my taxes before quitting that job and worked in this firm for few years cash in hand.
Since 2012 as I was granted Spouse visa I was working and paying my taxes properly.(Have done the necessary updates to HMRC and always updated them with online tax filling.

My question is,

I seen in the Naturalisation application they ask for the last 10 years history, will the be able to find that I have worked cash in hand for few years? I checked with HMRC my self recently and they confirmed that my tax is in order and there I do not owe any money to them.

Thank you very much