You definitely need to keep your kitten indoors until he's been neutered. It's not a bad idea to keep him in a bit longer too until he's matured and developed a natural wariness. Kittens tend to be fearless and are easily distracted, and so are much more likely to run into the path of a car chasing a leaf or something. If your other cat goes outdoors now there's no real need to keep him indoors because of the kitten, although it might prove difficult to let one out and keep the other in! If the resident cat is staying outside more because of the kitten I would consider confining the kitten to one room or part of the house, for some of the time at least, so that the resident cat feels less threatened.
Most people on here keep their cats indoors (including myself) but it is more common to allow cats outdoor access in the UK, as you know. If you think the area where you live is safe for cats then there's no reason why you shouldn't let your new kitten go outside. Cat proofing your garden or building a cat run in your garden is an alternative that would allow both your cat and new kitten to have some outdoor access while staying safe.