I think there is a higher probability of it looking strange to have a different wall material at each side of the drive, on a new job. The devil will be in the details and not enough is known. A plan sketch and calling out what is where might help.

People need to get over the mindset of a large tree in close proximity to a house is evil and forebodes all manner of doom! In many area of the country that are rather heavily treed naturally, trees planted or existing close to structures are commonplace. Tree roots are seldom an issue with foundation damage if the foundation is structurally sound - I'd be much more concerned about those of the water lovers and any underground plumbing. And it is almost impossible to replace the stately presence and shade generating capacity of a mature tree in one's lifetime if it is removed. It is very simple to have a tree evaluated by a certified arborist to confirm it is healthy and structurally sound before deciding whether or not to remove. We should be leaving as many mature trees as possible in place rather than cutting them down willy nilly for no valid reason other than we are fearful of its location.

The name for this type of stone facing is a masonry veneer cavity wall system. Its not structural but that term might be used because it is supported by a structural ledge at the foundation and by steel or concrete lintels at windows instead of being adhered to or hung on the backup wall. Its the most expensive way to add stone but it will last longer and look better than anything else. Whether or not you were robbed depends on what you paid for it. Its rarely seen because of the high cost. Fifty year ago it was the only option.

Can't really answer that as we have no idea of the breakdown of the challenges and costs associated with the construction of the concrete wall or how big this wall is. But the application of stone veneer, especially with a curved or rounded surface, is very time consuming AND labor intensive and labor is the biggest factor in landscaping expense. The more labor hours involved, the higher the cost. If you have concerns about the estimate you have been given, get a couple more from qualified masonry contractors or landscapers that do this routinely. Then pick the one that will provide the best work at the best price.