All perfect praise be to Allah The Lord of the Worlds and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
Light movements, like those made with one`s finger, even continuous, don`t nullify prayer, and the same ruling applies to little strong movement, such as stretching and closing the arm, deliberately or forgetfully; unless that was intended as some kind of play. However, repeated strong movement, intentionally or unintentionally, nullifies one`s prayer. For example, taking three consecutive steps or hits although there is no need for doing that. It also gives the impression that that person isn`t actually praying.
As for the second question, taking a Sutrah(Partition in front of one who is praying) in prayer is a Sunnah, not an obligation. In addition, taking three consecutive steps or more nullifies prayer. However, if the person had to do so, then he should make them inconsecutive or suffice with two.
Regarding the sound of the slight cough (Ahem) made while praying, if two sounds were uttered, then the prayer is invalidated. Nevertheless, if the praying person made that sound because he couldn`t breathe, then his/her prayer remains valid. This is because the Prophet (PBUH) said, "This prayer of ours is not the place for ordinary human speech, rather it is glorification and magnification of Allah (SWT), and reciting Qur'an."{Related by Muslim}. This is the reliable view of the Shafie jurists (May Allah have mercy on them). And Allah knows best.