David Warner recently scored 180 off 159 balls in a test cricket match against India, which ended up being the third fastest score of 180+ in terms of strike rate (runs/balls) (some older innings don’t have strike rate information). The only faster innings were the 222 scored off 168 balls by Nathan Astle vs England and the 293 off 254 by Virender Sehwag against Sri Lanka.
Michael Clarke scored his more recent 210 speedily too, with only 20 scores of 210+ having a faster strike rate (out of 210 other scores, some which have no data on balls faced). Clarke and Ponting posted a partnership of 386, which was Australia’s largest since 1946 and the 19th highest overall. Some records from day 2 of the 3rd test are here and here. It was the fourth time a triple century and double century were scored by a batsman in a series and the 15th time that two 200+ scores were posted by a batsman in a series (full list here).
Finally Clarke’s triple century in the 2nd test was the 25th overall and the 7th fastest in terms of strike rate (Hammond’s 336* was probably quicker but we don’t know how many balls he faced). He is one of very few players to average 45+ in both tests and ODIs.