Welcome! I'm so glad you decided to post here. And now you're entered into the drawing twice!
I'm so glad you'd rather keep your bunny a "house rabbit" too. They really can bring so much joy to our lives as well as they crave companionship and really need us. And since bunnies are great at keeping illness hidden, it's when we live with them in our homes, that helps us see those subtle changes that let us know something is wrong.
It's also great that your other half came home to a new pet and was happy! Whew!
Your bunny may continue to mark here and there until he is satisfied that he's got his point across that this is home. But you still want encourage good habits and if he gets out of hand marking you'll need to watch carefully, and scoot him back to the litterbox the moment you catch him in the act.
Regarding outside: Like gravehearted said, there are risks with being outside, (eg. wild animals can pass on diseases through urine etc that your bunny can then come in contact with in the grass)
But once you've weighed that and still want to have your bunny go outside, then just be sure it's pesticide free and stay clear of toxic plants. Here's a list of known ones by the HRS (I don't know if the list is U.S based) http://www.rabbit.org/chapters/san-...onous.html Domestic bunnies really are different than their wild cousins when it comes to this, and they can't tell the difference when it comes to what's good or bad.
Since I am never sure what plant is what, I just prevent my bunny from chewing on any plant, unless I know for a fact it is on the "okay to eat" list - like mint. In our back little area, we plant a little bunny garden with greens that that I know are good for them.
I don't use a lead. Our outside area is pretty secluded and secure, and it's not very big. You do have to be careful with any lead, even the harness type, because if your bunny is exploring and something scares him, he may run, pull on the leash, then feel like he's been caught and begin to panic and flip around. Which could lead to shock and/or injury. And you definitely don't want to use a neck leash.
With that warning said though, I do know someone who uses a full body harness type of lead(she also has a very mellow bunny) But she said she started by first putting just the harness on and letting him run around the house with it on. She'd feed him treats to get him to forget about it. She would put it on him everyday for about an hour until it just became no big deal. Then she put the leash part on, and helped him get as used to that as well. Bunnies will never be like dogs. They will go where they want to go, and she just uses the leash to make sure he doesn't get too far and or get into trouble.
She also only uses it in areas that she knows are safe. No other dog walkers, no cars, no sidewalk type walking.
Great questions by the way, and keep asking. That's what we're here for!. Soon it'll all be old hat, and you'll be able to help someone else out!
So great to have you here! Have a great weekend!