Yep, looks like a bud to me!

As to your other question, it really depends on how large of a tree you are talking about--that is how big is the trunk in diameter. Depending on the size of the tree, you might have a hard time getting a hole dug near the base of the tree without hitting a bunch of roots. If the tree is large, you could plant as much as several feet away from the trunk and guide the vines into the tree via a trellis, wire, a plastic coated gardening stake, or similar item. As far as shading the ground, I would suggest adding an organic mulch around the plant to conserve moisture and to add organic mulch to the soil as the mulch breaks down. A rock may provide some shade but will add nothing that aid in moisture retention in the soil as it decays.

Don't plant a Clematis at the base of a desert adapted tree unless you plan on putting it in a pot. Clematis need a ton of water and you could rot out a Palo Verde, Eucalyptus or Mesquite.

You are absolutely right. I decided to move the location of the clematis to the base of a short retaining wall instead. The roots will be in shade all day, and I can more easily control the moisture level. Thank you both!