I need entire process for the submission of a Splunk app to Splunk Cloud and what is the duration of these approvals
If it is a custom app, you can upload the app through the GUI. It will run the app against some vetting and provide you with a report on any issues and what needs to be fixed. In some cases, you may need to open a support ticket to get some things fixed.
Some supporting documentation at SplunkCloud service description for Splunkbase and private apps and Manage private apps in your Splunk Cloud deployment
How long it might take approximately for the support ticket to be resolved and the app to appear in the Splunk Cloud?