can you buy a iphone with just wifi? Like a ipad??

An iPod Touch will do everything an equivalent phone will do apart from making calls. It can use Facetime and Skype (obviously as long as it has a connection).

An old phone (apart from probably not having the same features as a modern iPod Touch) will connect to the mobile network unless you take the SIM out: I'm not sure whether its other facilities will work if you do that or whether it will simply demand you put a SIM in and sulk until you do.

I didn’t say it was better. You had asked about an iPhone or iPhone like device. The base price between an iPod touch and iPad mini is $200. You’d not mentioned what you wanted to use it for, and for many things (other then not being able to make cellular telephone calls nor send and receive SMS/MMS texts) an iPod touch is not unlike an iPhone in form and function.

Obviously for some things, the iPad mini/iPad Air/iPad larger display will be preferable. I would guess the iPod touch is most appealing to anyone who wants a small portable music/audio content player. In overall size and display size it would be most comparable to an iPhone SE. And in terms of cpu and performance, it would be comparable (with the recent update) to an iPhone 7.

In terms of cost, if in the USA you can also save with a refurbished device - Certified Refurbished Products - Apple

Yes (sort of). It's called an iPod Touch.

iPod touch - Apple

The iPod touch was just updated, btw, just a week ago - Music - Apple

No... But you can buy an iPod Touch, which is basically the same thing.