Is there any Rest API in Sitecore which can create, get, update , delete and publish items in web instance and Solr without writing any code
To create an item:
Edit an item:
Delete an item:
Run a Sitecore search:
Run a stored Sitecore search:
For more details you can refer: The RESTful API for the ItemService
This article given by
Sitecore contains almost all the
API calls that can help you to perform all the operations.
publishing, I found a good article you follow to publish an item on an API call.
Hope this will help you to start.