Can I use Time Machine but still be able to access deleted files on my Mac?
Yes, you can move files away from your Mac to an external HDD when using Time Machine.

The file will remain in the backups until the backup drive runs full and Time Machine starts deleting older backups.

Note however that the backup will contain a version of the file from before you’ve moved it to an external HDD. If you want to backup files on your external hard drive with Time Machine, you’ll need to remove the external drive from the list of exclusions in Time Machine settings.