Greetings from Helsinki! And tervetuloa.
A 60 min connection in your case will be just fine. I have flown the HEL-TLL-HEL hop frequently, and the FC-operated flights are usually on time. (FC = FinnComm Airlines, check
www.fc.fi)
You will not need to go through security at HEL.
At HEL, you will take the bus from the FC plane to a small vestibule, where you WILL NOT enter the baggage claim area with everyone else, but instead turn right at the entrance and walk up the stairs. (There is a sign but it is too easy to miss. If you enter the baggage claim area, then you will have to go through customs and security.)
On your way to your gate, you will go through immigration, which will not have long lines at 1-2 pm.
If and when your TLL-HEL flight arrives on time, a 60 min connection will not be a problem.
Please note that you will not receive AA miles for the TLL-HEL flights. The flights are AY flights operated by FC. They are not codeshare, there is no FC code on these flights, AY simply buys the service from a partner. And it was possible to get AA miles from these flights before, but for about 9 months or so, AA has refused to give the miles. If you succeed in getting the miles, please let me know and I will push them with my case
The AA departure to ORD coincides with the AY flight to JFK and these get feeder traffic from Moscow, Warsaw and the Nordic countries, among others. Should you miss your AA flight, they might be able to put you on the 4pm AY flight to LHR and get you to the US from there. This is what AY routinely does with their JFK passengers if the JFK flight is cancelled.