One makes up a missed prayer only by reciting an additional Amida and not by listening to the repetition; if, however, one did listen to the repetition during Shacharit to make up for a missed Arvit, he does not have to recite another Amida (Mishna Berura 108:5).
No; if, however, he became exempt only after the time for that prayer had begun, he should recite an additional Amida during the next Tefila, and have in mind that it should count as a voluntary prayer if it is not required (Halacha Berura).
Since the make up prayer must be recited after the prayer recited for the current obligation, a person in this case must recite a third Amida. Preferably, he should have in mind for the third prayer to count as a voluntary prayer if it is not required, unless he made a clear demonstration of the fact that he considered the first prayer the make up prayer, such as on Motza'ei Shabbat, if he inserted "Ata Chonantanu" in the second Amida but not the first. (Mishna Berura 108:7)
If he had in mind that the first Amida counts as his Mincha and the second makes up for his missed Shacharit, and he erred only in the first Amida, then he is required to repeat the Amida only once, to fulfill his Mincha obligation (Mishna Berura 108:9).
Yes, so long as the time for the current prayer has not passed; he should, however, stipulate that if he can no longer recite the make up prayer, his Amida should be considered a voluntary prayer (Mishna Berura 108:15).
In such a case it is proper to recite an extra Amida as a voluntary prayer with one's own requests added in the text of the Amida (Shulchan Aruch 108:5), and he must make a special effort to concentrate properly while reciting this Amida (Halacha Berura). One may not recite this extra Amida on Shabbat or Yom Tov, because voluntary Tefilot may not be recited on Shabbat or Yom Tov (Mishna Berura 108:18).
If he missed the prayer due to work he performed to avoid financial loss, he may make up the missed prayer, even though one should not miss prayer for the sake of avoiding financial loss (Shulchan Aruch 108:8). If he missed the prayer as a result of work he performed for the sake of increasing profits, he may not make up the missed prayer (Halacha Berura).
Although the Shulchan Aruch (108:7) allows one to recite a Tefilat Nedava in such a case, Halacha Berura writes that one should not do so, because nowadays we do not allow reciting a Tefilat Nedava unnecessarily.
He recites the morning Amida ("Yismach Moshe") twice; if he mistakenly recited the Friday night Amida ("Ata Kidashta") for either of the two prayers, he has nevertheless fulfilled his obligation, unless he had specific intent for the first Amida to serve to make up the missed Arvit prayer (Halacha Berura).
If he recited Havdala on Saturday night, then he clearly does not recite Ata Chonantanu on Sunday morning; if he has not recited Havdala, then he should add Ata Chonantanu in the second Amida recited on Sunday morning, though some authorities allow adding it to the first Amida instead (Halacha Berura).
If that night is also Rosh Chodesh, then he certainly recites a second Amida; if Rosh Chodesh ends at sundown, then he should recite an additional Amuda but stipulate that if the second Amida is not required, it should be considered a voluntary prayer (Shulchan Aruch 108:11).
Although the Shulchan Aruch (108:12) writes that one need not repeat the Amida in such a case, Halacha Berura rules that he should repeat the Amida on condition that if the repetition is not required, it should be considered a voluntary prayer.