The burning is how you know you're actually working and it doesn't hurt your legs. Since your muscles can only do so much in a day, the amount of burn you should feel depends on the ride.

For example, if you ride 100 miles or more or spend all day in the mountains, you don't want to feel much burning until maybe later in the day. For short sprints, there's nothing wrong with having your legs screaming.

It sounds like you need to do more physical labor. It's good for you to make all the muscles in your body feel like that sometimes.

Not my experience at all. Some of the worst pain I've ever felt was when I was in top form. The pain you feel is a function of how much you challenge yourself.