Now it's clearer. If this seems to be an important scenario for your team, you may want to consider the implementation enhancement by enriching the online data with offline data (read about data sources and transaction ID). As an outcome, you will be able to run a report in AA that will show you online and offline orders. Together with the segment (those who viewed a product but did not purchase) this should help recognise if significant amount of orders followed onsite search happen offline.
Scenario 2 is absolutely possible — just build a segment when a certain product had Product Views (or/and cart additions, checkouts, etc.) but was not purchased (order does not exist). This is probably one of the most commonly used scenarios for remarketing.
Whether there is a significant number of visitors who use the site to view the product then place their orders offline. If yes, cluster by visitors and/or by products to see the patterns, re-evaluate internal processes.
You can specify a certain product or product category if the scenario is to offer the product(s) the prospective customers probably were interested in. However, if you just want to build a segment of those who saw any product and did not purchase anything, then just do not specify the product in the segment.
If you could share more details regarding you business scenario/goal/problem, then the community may give you a better way to reach the desired goal using the existing functionality of AA.
When you say "a certain product" - do you mean one specific product? Sure, that's possible. I mean across the entire catalog, all the situations where any visitor viewed but did not purchase any product. Can you please clarify?
Let me give you two scenarios (I realize they are quite different in nature, but both stumped me in segment creation):
Visitor enters a search term captured in v1. The search results in several matches - exact and fuzzy, with the top result being the closest match. The top result is captured in v2. I want to create a segment that would include the visits where v1 matched v2. How?
Visitor views several products. Visitor does or does not place an order for one of these products, on this same visit or later. Say I want to create a segment for the visitor/product combination where there is a product view and no order for this product?