So, the quick answer to your question: yes, it is possible in both directions.
The simplest way is to use REST API.
For instance, to be able to push changes from your web site to the 1C:Enterprise infobase, you can publish and use the infobase's Rest API. If it is the default REST API, it does not require coding. Though, you may need to implement your custom REST API on the infobase's side, which requires coding efforts.
To push the data in the opposite direction (from the infobase to your web site), you first need to ensure your web site provides REST API and then on the infobase side, you need to implement the code that pushes the data to the web site.