Is there any big difference when it comes to designing for people aged 60 + and people aged 50?
Technological know-how, perhaps. For example, people who are 60+ might have never used a computer aside from simple tasks, but those who are 40-50 might have some experience with a bit more. This would depend on your user-base, of course.
You should also consider accessibility.
Should the design focus strong on the main target? Or should the design appeal to all target group, and maybe come to conflict with each other?
That might depend on how large the "main" target is compared to the rest - 90% of users? 51% of users? Ideally the design should appeal to any user, but if the site's slogan is something like "Retirement travel made easy!" then I would probably design more for that audience.
Since you also mentioned attracting a younger audience, I would think that the target isn't quite like the above, so you'd probably want to cover a broader audience.
Can good design for elderly people be visually appealing for a younger target group?
I don't see why not, but it really depends what you consider a "design for the elderly".