I agree with the other answer. It’s very steep for adults so a pushchair might be a good idea unless you want to carry them most of the way up or down. It’s also quite far down to the bottom

Definitely not! Ok to go down but very steep and uneven surface and you would need to be SUPER fit to push back up. Hard enough to walk up by yourself!

For some parts of the track yes - If you have 4WD robust buggy you could... but it is gravelly and could be slippery in wet conditions ... also you won’t be able to get down the stairs at the end and it is sort of narrow

Monday through Friday days, catch the Corstorphine bus, getting off on the last stop on Middleton Road near Milford Street), then walk about 15 minutes to the start of the track. We're not allowed to included URLs here, so just google "Dunedin bus schedule pdf" (see Routes 32 &33 on pages 70 though 71).

It's a reasonable taxi ride. There is no simple way from Port Chalmers. Perhaps see if a tourist bus operator goes there.

No we were there in September

Because it's a walking track. The track itself is maintained by the Dept. of Conservation, but the area around it is privately owned, not a publically owned park or nature reserve.