Some of my thoughts to your questions:
1. I'm a bit confused...if you can do 10 and 12 why not do 11? You're not trying to "pick a winner" but create a DF to estimate curvature over the design space. "Good" has nothing to do with it (and how do you know 11 is not "good"?). The less centered the center point, the more biased the estimate (the less rotatable the design). Of course, you can study any part of the space you'd like to, just realize you are making compromises and potentially biasing the results. Be careful of interpretation of the analysis. Why not do 10.5, 11.5 and 12.5?
2. I'm also unsure of your 2nd question and you may not find my comments useful. You will need make decisions regarding experiment design in the planning stage. For example: what effects will be separated, which ones will be confounded or partially confounded, how much practically significant amount of variation needs to be created, what is the current process variation and how stable is it, how will noise be handled (e.g., measurement error, raw material variations, ambient conditions, etc) and, of course, sample size (I'll leave the criteria for this to others). Many of the questions you need to answer in planning stage are currently unknown, and will likely be estimated. All you can do is due diligence. I highly recommend the practice of developing multiple DOE plans and comparing and contrasting them, evaluating the potential for knowledge gain vs. the resources required to execute. Predict every possible outcome and what you will do in each situation...then run it, analyze it and compare the results with predictions.
"All models are wrong, some are useful" G.E.P. Box