Who took the fewest innings to make 1000 Test runs at any point in his career?
And who was the first to get to 300 wickets in T20s?

Sunil Narine got his 300th T20 wicket recently, but another West Indian, and a Sri Lankan, got there before him • Randy Brooks - CPL T20 / Getty
You don't usually have to look beyond Don Bradman for this kind of record, and indeed he still holds the mark - he scored more than 1000 runs in eight innings between March 1929 (when he scored 123 and 37 not out in the final Test against England in Melbourne, and the 1930 Ashes series in England, in which he made 8, 131, 254, 1, 334 and 14. The Don added 232 in the final Test in 1930, finishing with 974 runs, still a record for any series.
The West Indian spinner Sunil Narine's 300th T20 wicket came up recently in Bangladesh, when he dismissed Worcestershire's Ross Whiteley during the match between Dhaka Dynamites and Sylhet Sixers in Mirpur.
I'm not sure whether you mean a team or an individual player - but it doesn't matter very much, as the answer is almost the same: India played 43 one-day internationals in 1999, and Rahul Dravid featured in all of them! Sourav Ganguly played in 41, while Mohammad Yousuf (Pakistan) and Lance Klusener (South Africa) also played 41 ODIs in 2000.
Jason Holder made 110 after coming in at No. 9 during West Indies' recent second Test against Zimbabwe in Bulawayo. This was the third occasion a Test captain had made a hundred from so low in the order - and the other two were both by the same man. Shaun Pollock scored 111 for South Africa against Sri Lanka in Centurion in January 2001, and a couple of months later added 106 not out against West Indies in Bridgetown.
England and Australia have both had a Test player called Moss - Jeff and Alan - who probably attracted this nickname as a matter of course. But the name was also attached to another player for a while: Percy Fender, the idiosyncratic Surrey captain who played 13 Tests for England - and, many thought, should have captained them. According to Richard Streeton's excellent biography of Fender, he acquired the nickname "Bill" after a mix-up over the payment arrangements for a farewell party during the First World War: "He remained 'Bill' to his closest friends. To his family, he was always 'George' [his second name]… At one stage in his cricket life, the nickname 'Mossy' Fender began to be used, but Fender never liked it and was thankful it never caught on widely."
Steven Lynch is the editor of the updated edition of Wisden on the Ashes