Hello Gopikrishna ,

Let's address each question separately:

Updating records through Batch Class and Trigger on the same object:
When you are updating records through a Batch Class and you have a Trigger on the same object that updates the same field, there shouldn't be any issues or errors as long as your code is properly written and handles the bulkification of triggers correctly.

Batch Class:
Batch classes are typically used for processing a large number of records in chunks. If you have implemented your Batch Class correctly and handle the updates efficiently, there shouldn't be any direct conflict or errors with the trigger.

Trigger:
Similarly, if your trigger is correctly designed to handle bulk operations, it should not cause any issues with the Batch Class update. It's essential to ensure that your trigger can handle multiple records in one go without causing any governor limit issues or recursive triggers.

It's important to note that the order of execution in Salesforce is well-defined, and batch classes usually run after triggers. So, any changes made by the trigger will be reflected in the Batch Class's processed records.

Using @future method in a Trigger to update the record:
Using the @future annotation inside a trigger to perform an update asynchronously will work, but you need to be cautious about recursive calls and governor limits.

The @future annotation allows you to run a method asynchronously in the background, outside the current transaction. If your trigger uses @future to update the same object's records, it could lead to recursion if the trigger is set up to fire on the same event that triggers the @future method. Recursive triggers can cause a chain of trigger and @future method calls, potentially leading to governor limit issues.

To avoid such problems, make sure you have a proper control mechanism in place to prevent recursive trigger and @future method calls. Additionally, ensure that the @future method handles bulk records efficiently to avoid hitting other governor limits.

If this helps , please mark this as Best Answer.
Thank you.