In order, more or less:

Just an ordinary wicker basket. Then we made improvements/alterations. It is tied down to the rack securely with cable ties. The wire keeping him in is also attached (underneath the basket) to the rack. We started out with it a bit tight, and the poor little guy couldn't breathe. He's pretty secure; he wouldn't go if he weren't. I'm aware of the dangers.

The harness is one made for securing the dog in a car using a seat belt. It fastens nicely to the bottom of the basket. I think I got it at Petco(?). It actually works better on the bike than in the car.

Squirrels. He's pretty short-sighted, I doubt he'll see 'em. He doesn't chase squirrels or rabbits in the back yard, so I'm not seeing a problem there. The wolf-hounds on the trail though...

We've talked about getting Doggles for Monty. That's up in the air for now.

DH does complain that Monty keeps goosing him, but if that's the worst of it, we can deal.

I had a Doberman once that was trained to the bike. She'd either heal or pull me up hills. We went miles and we both loved it. I don't know that I recommend it for just any dog, though. Vrka was incredibly trainable, and long-legged enough to match speeds with me. (I'm kind of slow.) For normal dogs, I think I'd use a trailer.