Thank you for your post to the message board. I'm forwarding the post to one of our Cork volunteers who may be able to assist with that query.
We have a Mayo volunteer who is also a Heffron and I'm forwarding the query to him for his reference. He may be able to assist you with your Heffron and Lavelle queries.
As to Monaghan, the records in many cases do not go back earlier than 1800, and a number of them are not online,so it may be a challenge. The surname Martin is very common in Monaghan,so you will need to have some more specific information such as a maiden name for Catherine or other family members for us to assist.
As to your queries for County Limerick, do you have any other information about Margaret Downey such as her maiden name? Any other information that you have would be a great help. You can post it on this thread and we will try to assist you further.