In order to migrate from M1 to M2, is it ok to do the migration process on a local environment and then just copy all M2 files and DB to my hosting server? or I need to do something on the host side before/after copying files and db?
Depends on differences of the environments and files you're going to move.
You should take into account user data (media files, configs).
If DB or other environment settings are different, you need to update it in app/etc/env.php All necessary information should usually be in this file. But if you used env variables for your website, you may need to convert them to m2 equivalent.