1. No default option for this in the current version and so it may require some code customization. However, advanced search is planned for implementation in version 3.1.
2. These may require some code modification.
3. This is used to be an option but removed in the current version. However, it is planned for reinstatement as users are requesting for it. Since there no encrypted files in Classsipress you can modify it the way you want it.
4. If you mean local environment, yes as some users have done.
5. If you have made some changes in the core theme files, they will be overwritten with new updates. However, you can implement child theme so your changes will stay intact even with updates.
Please help our moderating team work more efficiently by not sending us support questions via PM. You can read more about how AppThemes support works
here. However, you can send a PM to follow up and remind me if I missed your support request/thread.
Thank you and have a nice day.