4. I paid the premium one week late (or one month late). Is my policy still valid? Will the insurance company deny my claim if an accident happened immediately before my premium payment?
Often insurance companies would include a "grace period" clause in their insurance policies.
A "grace period" provides for a grace of, say, 30 or 31 calendar days (depending on the terms actually written in the insurance policy) to pay an overdue premium. The policy remains in force during the grace period. Thus, if a claim were made within the grace period, the insurance company is liable to pay the claim but the company has the right to deduct the amount of the overdue premium from the proceeds of the payment of the claim.
Note, however, that particularly in some commercial insurance policies, insurance companies may include a premium warranty clause, whereby the premium must be paid by certain date and if it is not paid by that date, then the coverage is void.
It is therefore important for you to check your insurance policy, to understand the terms which apply to payment of premium.