What topics should be discussed? Holidays? Family? Or just work? And
how much trust should be allowed?
Every situation is different. Every manager's personality is different. Everyone's level of trust is different.
I tend to get very friendly with the people who work for me - particularly those who have been with me for a while. For me, socializing at work, with people who work for me, and with people I work for, is an important part of what makes work rewarding. I would be much less happy going to work every day, if I couldn't discuss life with my work friends.
Regarding people who work for me, I know their families, they know mine. I've been to weddings, parties, and ceremonies with folks on my team. I've exchanged cards, I've exchanged gifts. I have long-lasting friendships with some.
When I talk with them in our weekly one-on-one meetings, I always ask how things are going in general, including outside the office. I ask about their spouses and children. I ask what they are doing for the weekend. I want to know about what is important to them.
When I hire someone new, I try to get a sense of how open they want to be with their lives outside of work. Only on a few occasions have I hired folks who aren't interested in talking about their lives, or hearing about mine. In those cases, I respect their desire for privacy.
While I'm an introvert by nature, I try to be as friendly as I can at work. With my managers, I try to get a sense of how much I like and trust them, and then open up about my life outside of work with them. With most of my bosses, I've felt free to be open and honest about almost everything. In just a few cases, I could tell they weren't comfortable or weren't interested, and so didn't share with them.
Only you can tell how much you trust your manager. Only you can sense what you are willing to share, and how much your manager wants to receive. Every manager-employee relationship is different.