Series was the term for both a batch of episodes of a programme, and the entire collection of episodes, in the UK.
Over the last ten years or so I have noticed that season is replacing series to mean a batch, but series is still being used.
I do not have a television, so I'm probably a bit out of touch with TV jargon, but certainly season is used with increasing prevalence online by the British, especially when referring to American shows.
Examples of use of series and season can be found in the following thread about Doctor Who?. For example: use of season, use of series (Layden, Dark Jedi, Hanners and PenguinJim are all British, as are some others)
Also this UK animé site uses season (see the side bar on the top left) and series (see the article) Anime Review: World God Only Knows, The - Season 2 - Eps. 1-7
As for writing academically, I think consistency is better. If you refer to a batch as a season then it is OK to do so for British shows.
I come across those words when reading novels all the time. However, they are almost never used in conversation.
The only one on the list that is somewhat archaic is "tarry", but its still a perfectly acceptable word that you might expect to come across in a new novel if the situation calls for it.
Best Answer
You might be over-thinking it. That said, I think I prefer the "#1 in a series" more than "#1 of a series". I would be more likely to use "#1 of..." when followed by a specific number, such as: "#1 of 5", whereas I would be less likely to use "#1 in 5".
"#1 in...", using in followed by an abstract quantity/collective sounds better to me, but that may just be my subjective opinion. For example: "#1 in (a) line" compared to "#1 of (a) line" or "#1 in a collection" or "#1 of a collection".
Also, the of gives it the feeling that it is a ranking or score rather than a position in a series.