I'm not sure whether any title agent could answer your questions with complete confidence, as the claims process is really the domain of the title underwriter.  As far as the process goes, I am not privy to any trade secrets, if there are any.  So no worries there about spilling any beans.  You can learn a lot just by reading the policy jacket and schedule B of the policy to see what's covered and what is not.

The hypothetical examples you provide seem unlikely to me but, I guess, possible.  In the case of the sudden appearance of heirs claiming a right to the property, I have a couple of thoughts.  First, the title agent would not insure title out of an decedent's estate without first having examined the concluded probate case.  That would have a judge's seal of approval in that any heirs were properly sought and accounted for.  Even if one was missed, the remaining heirs will have conveyed their rights to the property and the latecomer(s) would only be able to claim a right to a fractional interest in the property, if any.

In this case, I believe the best move on your part would be to notify the title underwriter as soon as you have knowledge of the competing claim.  Timely notice of a possible claim is always important, as the underwriter may find it in their intersest to defend and/or to cure any defect to mitigate their loss.  And they reserve that right.

In the case of the fraudulent purchase, I think the seller would need to be in on the scam also, and would have also had to have acquired the property fraudulently, and/or have an appraiser complicit in the scheme also.  Schemes such as this have worked, but have required crooks in pretty much every aspect of the sale, including mortgage broker, appraiser, real estate agent, title agent, and I don't know who all.  Otherwise it's a lot of different people who will have to be fooled.  If your second was closed and insured separate from the purchase, they would likely have had to get the dead guy's ID past two different notaries.

In any case, if the title policy insures that a decedent holds title to the property, I would say they have problems.  One out for the title company may be that, after the REO sale by the first mortgage holder who forclosed, there were no funds left to pay a second mortgage holder anyway.  So, you did not suffer any loss that you would not have suffered if the lien were perfected.  Depending on the circumstances, the title insurer could have plenty of other parties to answer to.

Again, the sooner you notify the better.  If your failure to notify in a timely manner cost them an opportunity to mitigate their loss, it could affect your claim.

If you want to get a better idea of some different title claims, and how they were resolved, get a hot cup of coffe in the morning and have a look at First American's Claims Chronicles.