If I have multiple connections setup to run every 24 hours on the same airbyte ec2 instance, will airbyte try to run them all at the same time or wait until one is complete before running the next?

If you had create 2 connections at 7pm then both will be trigger next day in parallel.

What if the instance is not big enough to handle parallel connections? Is there a way to set it up so that no more than a fixed number of connection runs at the same time?

Not right now, can you create a Github issue requesting this feature?