1- What does it mean that salatul Jaffar at tayyar can be counted as the nafilat of the day or night?
2- If I pray this prayer and skip out 4 of my 8 nafilah of dzuhr, would it still count as having completed the 51 rakat in a day if I pray all the others (salatul layl, and nafilah of the rest of obligatory prayer), or does it have to include all nafilahs of the obligatory prayers as well? (Talking about the many hadiths that states the importance of 51 rakats a day)
3- If I have little time, and wont have time to recite the tasbeehaatul arbaa during the prayer, can I pray the 4 rakat and recite the 300 tasbih on my way? *If allowed would I need wudu, and would it have counted as part of the prayer if I do?

1- It means you can pray it any time during the day or at night, and you can count it as the Nafila. So let’s you want to pray the Nafilah of night, Salatel Layl. It is 11 units, so you can pray Salat Jafar al-Tayyar, which is 4 units, and count that you have prayer 4 units of Salatel Layl, then you do 7 more and you would be done.

2- Yes you would be considered as completing the 51.

3- You can do that and it would qualify as the nafilah, but you may not get the full effect or praying Salat Jafar al-Tayyar. In any case, you don’t need to be on wudhu if you want to recite the 300 tasbih after the prayer