Back to top 2. Within reason, yes. Rocky ground, mud, sand, grass, snow etc are bread and butter. But be realistic. Steep mountain paths may be too much.
Swamps are out.
And remember, you will need to lift the pushchair over stiles, fences, walls etc. Hence a very lightweight model can be useful for serious outdoor use. Back to top I'll only use it around town. Because they are easy to push and manoeuvrable, even around town. Kerbs and uneven pavements are reason enough.