speeding convictions normally are not taken into account. However, any other conviction, dangerous/careless driving, manslaughter, dangerous parking, using car for illegal purposes are taken into account and all are examined on their merits.
penalty points are important as more than two speeding penalty points or nor wearing seatbelt could indicate a certain careleseness.
no insurer should refuse on grounds of age at this stage, but if an insurer refuses to quote or quote at normal terms for any other justifiable reason, then it also suggests that all is not well with the proposer.