If I browse the web on my iPhone while at work, but WITHOUT using their Wi-Fi, will they able to keep tabs on my internet history?

If I browse the web on my iPhone while at work, but WITHOUT using their Wi-Fi, will they able to keep tabs on my internet history?

No

No.

Nope

Not unless they somehow had cell capturing equipment like a StingRay capture tower. That is very unlikely unless you happen to work for the government.

If it is really YOUR iPhone - no.

If it is actually an iPhone provided by your employer for your use - yes.

Yes.

No.