Yes

Hi. The Bear Lake Trail would be a wonderful place for the kids to hike. I don't believe it was paved, but it's very flat with plenty of opportunities for the best family pictures! Keep track of them of course, but let them explore. You'll love it. The Rocky Mountain Nat'l park has a twitter page I believe where you can keep track of the crown level. The parking lot fills up fast, and you may have to park in Estes Park Garage and take the free trolley. We did.

Out and back.

It's a half mile. Less than 30 min, if you stop to take pictures.

We entered the park and took the shuttle from the park and ride lot. Only paid the $20/car. I would imagine you would still have to pay an entrance fee. No one gets into the park without passing through the entrance gates.

Springtime in the Rockies is highly unpredictable. In Colorado at that time of year, especially in the mountains, we never know if we'll get a summery day or get blasted by a blizzard until about 4 days out. Spring around here is when you really need to be prepared for all weather and conditions in terms of clothing and gear. Even if the weather is nice, the trails will probably be muddy; at higher elevations, they will probably be ice-packed. As far as crowds, you PROBABLY won't run into them so much during "mud season" because Trail Ridge Road will still be closed at that time. I usually expect April until mid-May to be the slowest time of year in general for Colorado tourist activities (with the exception being the Great Sand Dunes National Park - the weather is somewhat more predictable and pleasant during the spring in that part of the state).