Can dinosaurs be tamed while logged out

I've been testing this myself, and have come to the following rough estimate.
This is based on the sizes of creatures as defined by the size of their feces.

1. Small class dinosaurs are incapable of traversing one height walls
2. Medium class dinosaurs are incapable of traversing two height walls
3. Large class dinosaurs are incapable of traversing three height walls

It would seem however that the surrounding ground is important when trying to keep your base from being walked into.
Small hills near your base might enable medium size dinosaurs such as a t-rex to step over walls of two units high.

While I've seen a wild t-rex traverse a two height wall from an adjacent hill (to feast on our philo farm), I was unable to reproduce it on a tamed t-rex, so this might not be wholly conclusive and more in the realms of glitched pathing.

No they do not need to be mate boosted to lay eggs.

IME it may help in the frequency they drop though. Our mate boosted dinos seem to lay more eggs than our non-boosted dinos (another thought - our boosted are: dodo/dilo/raptor...stego/rex/trike not boosted, so maybe smaller dinos just lay eggs more often).

You really need to keep an eye on your dinos for finding eggs. They don't last long on the ground (5min for dodo, 15ish for rex), some of the smaller eggs can partially clip (and be extra had to see).