Purpose of the reduplication in 一步一步地往上爬 （A）别着急，一步一步地往上爬，爬不动的时候就休息一会儿。
（B）我请田芳一句一句地给我纠正。
I learned about the reduplication of Measure words (e.g:个个，天天  ) but these sentences use a different structure.
（1）What is the purpose of this reduplication? Can I write &quot;一步步&quot; or &quot;步步&quot;?
（2）Is the meaning of 一个一个 different from 一个个, 个个?
（3）Can all classifiers use this structure &quot;一...一...&quot;?
What dROOOze wrote is correct.  一步一步 is like step by step in English.  It can be shortened as 一步步，but it will lose the cadence and some effect.
You can probably apply this structure for every measure word, e. g.  一个一个，一升一升，一条一条，etc.
Well, unlike 一个个 or 一个一个,  个个 denotes the sense of every.  E. g.  我们班同学个个学习好 // Every student in our class studies well.