Use iPhone 6 as iPod (no carrier)

As long as its activated, Yes. All functions (except phone calls and sms messaging) are perfectly usable without carrier service. But you will need a functional sim card to activate it. Once activated, you can remove the sim card. The sim card does not need ot have active cell service on it. Just be a functional sim card from a supported carrier if the iPhone is locked to a carrier.

It should need to be activated if the previous owner correctly restored it and removed their account from it.

Some reading before buying:

Make sure the seller has followed this article completely before buying it:

What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support

Be familair with Activation Lock, as its very possible you can get an iPhone locked by it, and by extension unusable to you.

Find My iPhone Activation Lock - Apple Support

And by extension, read here for what to do from your side to make sure the iPhone you buy is not locked by Activation lock:

What-to-do-when-buying-second-hand-ipad-iphone-ipod-touch

I may receive some form of compensation, financial or otherwise, from my recommendation or link.

You want to check that the iPhone is not Activation Locked.

iCloud and Activation Lock: https://support.apple.com/kb/PH13695?locale=en_US

You cannot activate an iPhone without a sim. The sim does not have to be

associated with an active cellular account; however, if the iPhone is locked to a

particular wireless provider, the sim must be from that wireless provider.

Sure, will work fine. You will need a SIM in it to activate it with Apple. You can remove the SIM afterwards but it needs to be in the device for activation.