Are there any specific advantages to equipping specific pods that only exist in combination i.e. the particle accelerator and telescope together lets you Death Star Superlaser? Are there any combinations that are incompatible outside of size restrictions?

Yes, although at the moment there is nothing so exciting as creating a superlaser! The most advantageous pod pairing will be adding analysis to pods that generate data; so having more computer equipment to study the data your telescope array generates would be a benefit. (The most obvious connection is pairing the medical center with the landing bay, which connects the two directly and allows you to import patients.)