1)Are there other synergies besides cost and revenue you need to think about in M&A cases?
Yes and no. R and C is a fair structure to have. However, the more you can show your industry and case-specific thinking the better. For example, if we're a healthcare provider + insurer and we're looking to buy a wearables company, an excellent candidate would break it down by considering product bundling/ecosystem synergies, customer sharing synergies, and data analytics synergies. They would refer to these in terms of Revenue uplift and cost reduction.
In summary: Please don't just say "i want to look at the revenue and cost synergies"! You need to categorize and identify them based on the specific case on hand!
2)Are these different from synergies brought in by a PE firm?
PE firms do not bring synergies (most of the time)
3) What is the best way to segment synergies, by looking across value chain? For eg, in costs, looking at R&D , then production, distribution etc..?
See point #1. But yes, value chain can be one way.