How many batters have scored four or more centuries in three successive Tests?
And is there a Test cricketer who also played tennis in the Davis Cup?

Everton Weekes (right) scored five hundreds in four successive Tests in 1948-49 • Getty Images
This purple patch by Jonny Bairstow has brought him 589 runs from 578 balls in his last five Test innings. After being out for 8 against New Zealand at Edgbaston, he added 136 in the second innings, then hammered 162 and 71 not out in the third Test at Trent Bridge. After that, he hit 106 and 114 not out against India at Edgbaston.
England rattled along at 4.93 an over in that remarkable chase at Edgbaston last week. Only two successful fourth-innings chases of more than 300 were completed more quickly, and neither involved quite as many runs: Pakistan's 302 for 5 to beat Sri Lanka in Sharjah in 2013-14 came at 5.25 an over, while West Indies' 344 for 1 against England at Lord's in 1984 came at 5.19 an over.
You're right that the long-serving wicketkeeper Imtiaz Ahmed appeared in all of Pakistan's first 39 Tests, from their inaugural match in 1952-53 to the first Test in England in 1962. That was indeed a record at the time, but has since been surpassed by Alistair Campbell, who played in all of Zimbabwe's first 56 Tests; Andy Flower appeared in their first 52 as well. Next come Habibul Bashar, a fixture in Bangladesh's first 30 Test matches, and the Zimbabwean Grant Flower (also 30).
Barry McCarthy's 110 - more than twice as many as he had made in any other senior innings - came for Leinster Lightning against Northern Knights in Ireland's Inter-Provincial one-day tournament at Pembroke CC in Dublin last week. His runs came from 59 balls, and included ten sixes.
It isn't true - but someone did come very close: Leslie Poidevin was Australia's 12th man for the first Ashes Test in 1901-02 and, after England won by an innings in Sydney, was in line for a probable debut in the second match in Melbourne. But he picked up a finger injury in practice, and was replaced by Reggie Duff - who scored a century on debut as Australia squared the series. Duff claimed a regular berth, and Poidevin's chance was gone.
Steven Lynch is the editor of the updated edition of Wisden on the Ashes