Traffic Offence (CU 50)

HI,

I'm on ILR and eligible for naturalization last year i.e. September, 2015 but I didn't go for naturalization. I had a traffic offence CU 50 – Causing or likely to cause danger by reason of load or passengers (I had an extra passenger in my car back seat). This happened in December, 2015. I have received a letter with conditional offer of (£100 fixed penalty and 3 points on driving licence) or (challenge my offence in court). So I have accepted the conditional offer by paying £100 and posted my DL to them. They have sent my DL back after processing it. My questions are,

Can I apply for naturalization now?
How likely they will reject my application because of traffic offence?
Are there any successful applications with CU 50 offence and the application made within 12 months of the offence date?

Please help…

ILR – Sep-2014
Eligible for Naturalization – Sep-2015
Traffic Offence – CU 50 in Dec-2015

Thanks,
Naresh