Hello and welcome to the forum. I am very sorry that you joined under the tragic circumstances of your loss. It mirrors somewhat my journey to the forum and it has been for me, a wonderful insight into the world of rabbits, from people who are always on hand to give you advice and support you.
I am sorry that you have lost one of your buns, and although you say they were not bonded, rabbits do go through a grieving process. Some rabbits handle the process, others dont and can, sometimes go into stasis (where they stop eating and pooping). It can, if not acted on quicly, cause death so one thing I would suggest you to do over the following days is to monitor your surviving rabbit very carefully for signs of loss of appettite and also poops. He will feel a loss but you are the eyes and ears of him and so you needto watch his body language.
I would suggest a full course of vaccinations as suggested in previous posts. These will protect your rabbit and also it would be helpful to have some insight as to perhaps how or why your other bun passed. If he died suddenly, then it may be the cause of VHD. So a vet check would be helpful for your surviving bun.
They can live in some cases, as long as 10 and posibly 12 years depending on their environment and health. There really is no definitive age on how long they live.
Bringing him indoors? Well, it is an option although if he's been used to being outdoors, he may not take to it immediately so you could perhaps try introducing him into the indoor living area slowly - maybe an hour or two at first. It is important he feels companionship - rabbits are extremely sociable and benefit most from being in groups - two or more. A bunny companion is the best support for your rabbit and rescue centres provide a wealth of expertese and help. And you would be giving a rescue bun a second chance in life - which is immensely satisfying.
You could get your bunny some toys to relieve the boredom and perhaps a snuggle toy like a toy soft rabbit? Give him loads of extra attention and make him feel special because like you, he will be grieving and upset so he needs the support from you.
Bunnyproofing your house? That's a tough one. Rabbits primarily love to chew. They don't do it on purpose but in a home, they can cause problems. Wires and cables that are reachable will look like roots to your rabbit and it's instinct is to chew them. So you need to ensure there are no wires or cables that your bun can get to. Telephone cables, tv wires, ariel leads, computer/laptop leads, hub connections, and anything electrical. Some rabbits chew furniture so be mindful of that. Wood especially. A few rabbits (some on this forum) like to re-decorate and have a liking for chewing wallpaper and skirting boards and mine likes to chew the plaster off the walls.
Making a safe area using high wire caging - like a dog pen or similar, will provide a safe inside environment and many rabbit owners on this forum have the most wonderful indoor areas for their rabbits. Maybe look through the threads in the chat part and see what we do for our indoor rabbits. Flooring is also important as rabbits can slip and cause themselves injuries from this.
I hope that you can find something to help you with my posts and please let us know how your rabbit is doing and please keep an eye on him and get him both vaccinated and also neutered. It will be in his very best interests at this stage.