Case
How to be a likeable or chill teacher while maintaining respect from the students?

I don't really see myself as a strict individual. I would feel like I would enjoy a free flowing classroom and enjoy certain comments by students that might be considered interruptions by other teachers. However, I don't want it to be seen as I don't care about any rules in general or I want people to make small comments all the time. How do you think you can maintain the respect from students while being not as strict as other teachers?

Solution #1
I think the key is being consistent. Tell them when you are being serious and flippant comments are not allowed and what will happen if they keep on. Then, follow through on it if the comments continue. I had a teacher that was pretty chill like that but when he needed us to be serious he warned us at the beginning of class and we pretty much complied.
Solution #2
Through my few experiences with managing classes so far, I can say that students will respect the rules if they understand them. Being a "chill" teacher does not have to go hand in hand with a rule-less classroom. Go over rules at the beginning of the year, and explain /why/ each rule exists. Students are a lot more open to following the rules if they understand why they are in place. You will seem more likeable as a result too ("I don't mind if you guys talk, but we have to keep it at a whisper so that we can all hear one another, and I can still get your attention without yelling. I don't //want// to yell at you guys ;) ").
Solution #3
Set expectations for your classroom early on, and don't bend rules. At the same time, listen to your students and ask for their opinions. Being there for them is a big way to be likeable.
Solution #4
Setting clear expectations with students from day one will help them to recognize that even though you are "cool" that you still need to be treated with respect and kindness.
Solution #5
Overall, in this specific situation I think it's most important that your students show respect for you. In my own experiences, I know I always had more respect for my teachers I viewed as friends because they made school feel like a safe environment to have fun and learn. I don't think it's a bad thing whatsoever to be more flexible when it comes to classroom rules; however your students should know to listen when it's time and take what you say seriously. As long as the conversations end when you ask, I think your students are successfully showing respect for you and your classroom.