A Constant Scan is basically adding a column to the data being passed around. Look at the properties and it will define what it is adding. It may be something cryptic, in which case you'll have to look through the rest of the operaters to understand what that represents, or it could be really clear, an alias or something in the T-SQL.
You can use PasteThePlan. You can also zip the plan and post that zip file (which, a lot of people aren't crazy about, but it's one way to do it).
Something is of use in the NCI or the execution plan wouldn't reference it. It's scanning for a value or something that it can use in filtering elsewhere in the plan. I can't say much more without seeing the plan itself.
Also, no idea what you mean by an "anomaly in an estimated plans". All plans are estimated plans. An actual plan is just an estimated plan with the addition of runtime metrics. Extremely useful, don't get me wrong, but not radically different from an estimated plan. It's the same plan, plus runtime metrics. That's a huge point that people frequently lose the thread on. Can you see a difference between an estimated plan and an actual plan? Yes. But that is the result of recompiles normally, so, not some kind of bug in estimated plans.
The naming convention, estimated versus actual, leads to confusion. I have taken to referring to execution plans, and execution plans with runtime metrics. Makes things much more clear. However, people don't understand me, so I have to then say (estimated) and (actual) to clarify. Ugh!
Anyhow, for detail, make the plan available somehow.