7 minutes for train transfer enough?

That is enough time That is a small station
https://it.wikipedia.org/wiki/Stazione_di_Levanto
and your connection is on the same platform. if you miss it you can get on the next train

Yes, that is normal. Click for photo of Levanto station. And another photo here.

The two trains may stop parallel to each other on opposite sides of the same platform so it will only be about 10 steps. Worst case you go down to an underpass under the tracks, and up to the other platform.
The two trains are designed to connect, it is waiting for passengers off the first train.

Thank you both, Jazz+Travels from Chicago and Chris F from Basel, Switzerland. We appreciate your answers more than a simple grazie mille conveys.

I found frequent delays when taking trains up and down the Riviera last May. So I wouldn't be surprised if you miss the connection. On the other hand, the train you are connecting to may be delayed, too!

But yes, there are plenty of trains between Levanto and Riomaggiore. Assuming the one you are booked on is a regional train, you want to take the next REGIONAL train not an IC train (with reserved seats), FYI. First of all, not all trains going south from Levanto even stop in Riomaggiore. But any regional train should. There will be a big printed schedule up at the station on each platform that will show the schedules of each train departing from that station - may be new to you if if this is your first time in Europe. If you have a working smart phone (recommended), you can install the Trenit app on it and use that to monitor real-time train delays ("Is my next train delayed too?") and platform info. But you can also use it to find out when the next regional train going south (toward La Spezia) is due. Very handy.

Thank you Andrew from Portland, Oregon for your helpful reply. I have downloaded the Trenit app. If we miss the connection in Levanto will we need to buy another ticket?

Liguria (the Italian state where Levanto and Riomaggiore are located) has its own time limit for regional trains. I believe for Liguria, the ticket is valid on any train for 75 minutes after the time of the train listed on the ticket. Your last train is probably the Cinque Terre Express (a regional train) and it goes every 30 minutes from Levanto. So if you did miss the connection, your ticket is still valid for the next CTE. There are also regular regional trains, at least 1 per hour in addition to the CTE that will get you to Riomaggiore.

In the case of a major delay that is Trenitalia's fault, you can get the ticket reissued.

Edit, I should add that if you buy the ticket on-line, the last regional leg will be pre-validated for 4 hours from the time of the train listed on the ticket. I believe that supercedes the Ligurian rule of 75 minutes for tickets bought from a vending machine or ticket window and need to be validated in the platform stamping machine.

If we miss the connection in Levanto will we need to buy another ticket?

No, tickets for regionalle trains are valid for a 4-hour window.

Chris, even if he called Liguria a "state" Sam is right about the 75 minutes rule.

I should add that if you buy the ticket on-line, the last regional leg will be pre-validated

This is the first time I hear about this difference between the web and the counter, did you experience it in person? Did you receive a pdf ticket for regional trains running in Liguria that said "valid for 4 hours"?

Sorry about the incorrect terminology, but when communicating with the OP, who has stated it will be the first time in Europe, I thought it best to use a term that is the rough equivalent to a US state.

From the Trenitalia Conditions of Carriage or Regionali, Section 4, UTILIZZO, CONVALIDA E VALIDITÀ DEI TITOLI DI VIAGGIO, Paragraph 3, Validità
http://www.trenitalia.com/tcom/Informazioni/Condizioni-Generali-di-trasporto/Parte-III-Trasporto-Regionale

Now maybe that is just my interpretation. I am not an Italian lawyer, nor do I play one on TV.

Sorry, I wasn't aware Liguria had its own rules.

All Italian Regions set their own rules re Regional services because they pay 80% of the actual costs to make Regional trains running. Most just follow the old "4 hours" rule, but some stereotypes are true... :D

For the same reason, and after reading Trenitalia's rules linked above, I think there is no difference between the tickets purchased online and those purchased at the counter: 75 minutes for all when the journey is shorter than XYZ* kms.

*XYZ means: I can't remember the real number.

I think I recall 50 km. But best to follow Dario's advice. Eye's on the ground.