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!
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