All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Muslims are commanded to call people to the Oneness of Allaah before calling them to any other obligation. The evidence for this is that the Prophet clarified such order when he sent Mu'aath Ibn Jabal to Yemen saying to him: "Indeed you will come across the people of the Book, so the first thing you should call them to, is to believe in the Oneness of Allaah, if they acknowledge this, then inform them that Allaah ordained them to perform five daily prayers…" [Al-Bukhari and Muslim] This narration clarifies the principles of Da'wah (calling people to Allaah) and that the Daa'iyah (the person who calls people to Allaah) should first start with the most important thing and then gradually move to other matters.
The evidence proving that calling people to Allaah is an obligation is the saying of Allaah (which means): {Say, "This is my way; I invite to Allaah with insight, I and those who follow me. And exalted is Allaah; and I am not of those who associate others with Him."} [Quran 12:108]. Moreover, the Prophet said: "Convey on my behalf even if it is (only) one verse (from the Quran)." [Al-Bukhari] For more benefit, please refer to Fataawa 90426 and 87210.
As regards the rulings of Da'wah, they differ according to the difference of the people, environment, circumstances and time. For some people, Da'wah is an individual obligation, this is when there is no one else who may do this task. In other cases it becomes a communal obligation (which if carried out by some competent individuals, other individuals are not obliged to do it) and so the individual obligation is waved off. This, of course depends on the situation of the person who invites to Allaah and the person who is invited and other relevant circumstances.
As regards being questioned about it on the Day of Judgement, then some interpreters of the Quran attributed some Quranic verses to it. For instance, Ibn Al-Qayyim said: 'Muqaatil interpreted the saying of Allaah (which means): {…and We took from them a solemn covenant. That He may question the truthful about their truth.}[Quran 33:7-8], to refer to the Prophets in conveying the Message.' Moreover, Mujaahid said that the verse means that Allaah will ask the people who convey on behalf of the Prophets, whether or not they conveyed from the Prophets. Similarly, Allaah will ask the Prophets whether or not they conveyed the Message of Allaah. The most authoritative opinion about this is that the verse refers to both meanings, and the word “truthful” refers to the Prophets and those who convey on their behalf. Therefore, Allaah will ask the Prophets about conveying His Message, and will ask the people who convey on behalf of the Prophets, then Allaah will ask those to whom the message has been conveyed about their response to the Messengers. Allaah Says (what means): {And [mention] the Day He will call them and say, “What did you answer the messengers?”}[Quran 28:65]. This is indeed the meaning which was provided by At-Tabaraani, Ibn Al-Jawzi, Ash-Shawkaani in their Tafseer (interpretation of the meaning of the Quran).
Additionally, it is confirmed that the Prophet said: "Indeed Allaah has ordered me and He will surely question me whether or not I conveyed the Message to His Slaves, and I will respond to him: ''O my Lord, I have indeed conveyed the message to them.'', so those who are present amongst you should convey the message on my behalf to those who are absent." [Ahmad and Al-Haakim]
Finally, it should be mentioned that we have not come across a text which clarifies whether the questioning about Da'wah is after the questioning about the prayer or before it.
Allaah Knows best.