Any BB-proprietary services (e.g., email, native browser, BBM, etc.) will require a proper BIS plan from your carrier, even if you only use them via WiFi. Many add-on and 3rd party apps likewise require a proper data plan, while others can be configured to truly use WiFi only and not require a data plan. The requirements are always changing, so you are best off to make a list of those specific things you desire, and then inquire about each specifically rather than asking about "applications like". If they are not a BB-developed app (there are very few of those), then you need to inquire of the app developer directly.
As for WhatsApp, I have a recollection that it requires a BIS plan, but I don't use it so can't say specifically. But, again, asking that app developer would be your best bet.
Occam's Razor nearly always applies when troubleshooting technology issues!
If anyone has been helpful to you, please show your appreciation by clicking the button inside of their post. Please click here and read, along with the threads to which it links, for helpful information to guide you as you proceed. I always recommend that you treat your BlackBerry like any other computing device, including using a regular backup schedule...click here for an article with instructions.