Well firstly the IVA/BR should not have any effect on your car insurance but you could always give them a general call and double check.
Mobile phone contracts are dependent on the company, i had an o2 contract and when i told them i was BR they put a stop on my mobile and said the only one i could have now would be pay as you go and the bill which would show the money owed from the rest of the contract term would go into the BR, an IVA i would have thought you would be ok to keep the contract and some on here that have gone BR have kept their mobile contract too,i think i got the short straw.
As for the house unless your on the mortgage then the IVA/BR should have no effect on your parents at all.
They can if they are worried disasociate themselves from you by contacting the credit ref agencies.
Take Care
Jo x
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