1) moving house has no negative impact, unless its a regular thing. Two addresses in the last three years, for example, would be deemed quite normal. Anybody assessing you for credit may ask for proof of residency (up to date utility bill for example) for your new address, until you show on the electoral roll.
Electoral roll records are normally sent to credit reference agencies every January, around 6 months after council records are updated.
Your two months arrears will show now as settled, but will not drop off your credit file for around 18 months.
Every payment you make on time will gradually improve your credit file, with the 12 month mark being the most significant, in terms of improving credit standing. Lenders mainly look at the last 12 months payments.
Get a copy of your file at
www.experian.co.uk
www.equifax.co.uk
Good luck, hope this helps