Star Trek: Deep Space Nine (1993–1999)
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The reason for TOM Riker's reaction to O'Brien was that he didn't want the chief to reminisce about events that took place between O'Brien and WILL Riker on board the Enterprise, as TOM Riker would have no knowledge of such events and would possibly be exposed. Giving the Chief the cold shoulder allowed Tom to go about his business without O'Brien uncovering who he really was. Edit
Unfortunately, they aren't. This applies to the DVD releases. Due to Britain's strict policy some episodes had to be cut in order to avoid a higher rating. Because of cost-efficiency, these masters were used for nearly all European DVD releases as well. To the Death (1996) and Sons and Daughters (1997) are affected. One can find a detailed comparison for 4.23 here and for 6.03 there. Edit
Yes; however, these earlier episodes will help to understand what's happening in DS9.
Worf's backstory and rivalry with Duras: Sins of the Father (1990), Reunion (1990), The Mind's Eye (1991), Redemption (1991) and Redemption II (1991).
Tribbles: The Trouble with Tribbles (1967)
Koloth: The Trouble with Tribbles (1967), Kor: Errand of Mercy (1967) and Kang: Day of the Dove (1968) (Dax's Klingon friends)
Tom Riker: Second Chances (1993)
Mirror universe: Mirror, Mirror (1967)
Battle of Wolf-359 and Jennifer Sisko's death: The Best of Both Worlds (1990) and The Best of Both Worlds: Part II (1990)
Cardassians: The Wounded (1991), Chain of Command, Part I (1992), Chain of Command, Part II (1992), The Chase (1993), Parallels (1993), Lower Decks (1994), Journey's End (1994), Preemptive Strike (1994)
Bajorans: Ensign Ro (1991), Disaster (1991), The Next Phase (1992), Preemptive Strike (1994)
Ferengi: The Last Outpost (1987), The Battle (1987), Peak Performance (1989), The Price (1989), The Perfect Mate (1992), Force of Nature (1993), Bloodlines (1994)
Chief O'Brien: The Wounded (1991) (hatred of Cardassians) Data's Day (1991) (wedding) Disaster (1991) (birth of Molly)
Additionally, there is the crossover episode Birthright, Part I (1993), where the Enterprise-D docks at Deep Space Nine, and Dr. Bashir assists the TNG crew. Edit