Is it possible to use an iPad mini in place of a phone all the time?

WiFi Only models of iPad have no Cellular radio components at all. If instead you have added a DataSIM and Cellular plan to a WiFi+Cellular model of iPad, the number associated with the SIM card is only used to identify your account for billing purposes. This number is not used for making calls or sending messages.

An iPad, whether a Cellular model or not, is not capable of directly accessing Cellular Voice or Messaging features. An iPad with Cellular connectivity alone can only access IP-data services. An iPad is not, and can never be, a standalone substitute for an iPhone. 

However, If paired with an iPhone, the capabilities of iPad significantly broaden to include access to Cellular Voice and Messaging services of the associated iPhone - relayed to the iPad over WiFi using Apple’s continuity features. For the most part, an iPad using Continuity is able to access Cellular calling features, of the iPhone, when both the iPad an iPhone are in close physical proximity and are connected to the same WiFi network - but this is not the end of the story.

Now, if your both your Cellular Carrier and your calling plan support WiFi Calling, your iPad can make and receive calls independently of the iPhone - in some cases, even when the iPhone is switched off, elsewhere, or using a different WiFi network. Not all carriers support full WiFi calling - and many Carrier representatives don’t technically understand or acknowledge its existence.

More information about Continuity and the relevant Cellular services can be found here:

Continuity

Use Continuity to connect your Mac, iPhone, iPad, iPod touch and Apple Watch – Apple Support

SMS/MMS Messaging

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

WiFi Calling

Make a call with Wi-Fi Calling – Apple Support

When correctly configured, the iPad FaceTime App provides access to Cellular Voice Calling features - whilst Messages supports SMS/MMS messaging services.

So, in conclusion, if your own Cellular Carrier and tariff support WiFi Calling, it is theoretically possible to configure WiFi Calling service for your iPad. After WiFi Calling is enabled and configured, your iPad can continue to make and receive cellular calls independently of your iPhone whilst connected to a WiFi network.

I hope this information and clarification is helpful in understanding the capabilities of both your iPad - and if you have one, your iPhone.

No, not for phone calls or SMS/MMS messages. You can only make/receive phone calls and send/receive messages from an iPad if you do it through an iPhone by using Continuity. See: Make and receive phone calls on Mac or iPad - Apple Support and Forward SMS/MMS text messages from your iPhone to your Mac or iPad - Apple Support