Is Anderson the oldest seamer to take a Test five-for?
And how many players took a wicket with their first ball in Tests but none after that?

James Anderson takes a wicket in the Mount Maunganui Test. He is currently the third oldest non-spinner to take a Test five-for • AFP/Getty Images
Jimmy Anderson finished England's crushing victory in Mount Maunganui at the weekend with 4 for 18 in the second innings. He's already the third oldest non-spinner to take a Test five-for - he was about a month short of his 40th birthday when he claimed 5 for 60 against India at Edgbaston last July. Ahead of him lie the South African medium-pacer Geoff Chubb, who marked his only series - in England in 1951 when he was 40 - with 6 for 51 in the third Test at Old Trafford, and the legendary England bowler Sydney Barnes, who was around two months short of his 41st birthday when he took 7 for 56 and 7 for 88 against South Africa in Durban in 1913-14. Anderson will be older than Barnes if he can conjure a five-for in this summer's Ashes series.
The match you're talking about was last week's T20 World Cup match in Paarl: New Zealand's chase got off to a disastrous start when both Suzie Bates and Sophie Devine fell to the first ball they faced, in Megan Schutt's opening over. We don't have balls-faced data for all matches, but this looks like the second such instance in women's T20Is: both Mexican openers were run-out for ducks after facing one ball against Brazil in Lima in October 2019. I suppose some might not consider being run-out first ball as a golden duck.
The Guyanese slow left-armer Gudakesh Motie had match figures of 13 for 99 (7 for 37 and 6 for 62) in only his third Test - West Indies' innings victory over Zimbabwe in Bulawayo last week. These were indeed the best by a West Indian spinner, beating Sonny Ramadhin's 11 for 152 against England in a famous match at Lord's in 1950.
There are now 20 men who are known to have taken a wicket with the first ball they bowled in a Test. Two of them never took another one. The New Zealander Dennis Smith took the wicket of Eddie Paynter with his first ball in the match mentioned in the first question above, in Christchurch in 1932-33, but finished with 1 for 113 and was never selected again. Much later, in 2015-16, South Africa's Hardus Viljoen dismissed Alastair Cook with his first ball in a Test, in Johannesburg. He also hit his first ball for four when he batted, but never played again.
The Shaheed Veer Narayan Singh International Stadium in Raipur was the venue for the second one-day international against New Zealand in January. It was actually the 50th different Indian ground to stage a men's one-day international, or the 53rd if you lump in Tests and T20 internationals as well. At the moment, Raipur is one of five Indian grounds to have held a solitary men's international, after the Bombay Gymkhana (a Test in 1933-34), the University Ground in Lucknow (a Test in 1952-53), Ahmedabad's Sardar Vallabhai Patel Stadium (an ODI in 1981-82), and the Indira Gandhi Stadium at Vijayawada (an ODI in 2002-03). Eden Gardens in Kolkata comfortably leads the way with 84.
Steven Lynch is the editor of the updated edition of Wisden on the Ashes