Q:

Minimum user profile to connect to Connected App

I am new to Salesforce. I deployed a Connected App with Full Access scope. I was able to connect from my app via the Connected App and query data on my developer instance of Salesforce. I could also create a user profile and assign that user profile to the app through which I connect. Firstly, if I connect through the connected app with the custom user profile I created, can my app only query the data which that user profile has access to?
Then, I'm trying to also connect through my Connected App of a trail version of Salesforce, since I'll have to explain to my client what the minimum requirement settings is. Although the user from the trail instance can authenticate in my app, I cannot query any data altough my I think the user profile settings is correct. I'm using sosl and soql queries. 
profile

And the app settings:

What minimum settings do I need for the user profile assigned to the connected app to be able to query contact information through sosl and soql in my app? And do I need 'Full Access' scope or only 'access to data via the web'?

A:

To read, update or delete you will need permission "Customize Application" AND either "Modify all data" or "Manage Connected Apps". As a best practice "Modify all data" should be avoided. For more details about "Connected Apps" visit this link. This link has all details about user permission needed for "Connected Apps"

A:

The problem isn't your profile, but rather the Trial Edition that you've signed up for. It appears that your trial is a Professional Edition trial, which doesn't have the API by default. Your client needs to have at least Enterprise Edition. You should be able to contact Sales and either have your trial upgraded to the correct version, or get a new trial with the appropriate edition. I arrived at this answer by noticing that your profile screenshot does not include the "API Enabled" permission that would normally be found in Administrative Permissions, which suggests that you do not have the API to begin with.
The minimum configuration you would need to use a Connected App would include: (a) Connected App assigned to the profile, (b) API Enabled, and (c) View Object permission for any type of object you're trying to query (e.g. if you want to query Accounts, you need to have the View Accounts permission enabled). This profile would be able to query records if you had API access, or if your Connected App was whitelisted by a Security Review.

