Praise be to Allaah.

Firstly: 

It was not permissible to address the Prophet (peace and blessings of Allaah be upon him) by saying “Ya Muhammad” during his lifetime, because Allaah says (interpretation of the meaning): 

“Make not the calling of the Messenger (Muhammad صلى الله عليه وسلم) among you as your calling one of another”

[al-Noor 24:63]. 

Al-Dahhaak said, narrating from Ibn ‘Abbaas: They used to say Ya Muhammad, Ya Aba’l-Qaasim, but Allaah told them not to do that, out of respect to His Prophet (peace and blessings of Allaah be upon him). So they said Ya Rasool Allaah (O Messenger of Allaah), Ya Nabi Allaah (O Prophet of Allaah). Mujaahid and Sa’eed ibn Jubayr said something similar.  

Qataadah said: Allaah enjoined that His Prophet (peace and blessings of Allaah be upon him) should be treated with respect and venerated and honoured as a leader. Muqaatil ibn Hayyaan said: Do not address him by name when you call him and say Ya Muhammad, and do not say Ya Ibn ‘Abd-Allaah. Rather address him with honour and say Ya Nabi Allaah or Ya Rasool Allaah. 

Maalik said, narrating from Zayd ibn Aslam: Allaah enjoined them to address him with honour. 

So the Prophet (peace and blessings of Allaah be upon him) should not be addressed by name only, rather it should be said: Ya Rasool Allaah, Ya Nabi Allaah. 

Secondly: 

It is not permissible to call on the Prophet (peace and blessings of Allaah be upon him) in du’aa’ after his death, because du’aa’ is an act of worship that can only be directed to Allaah. Allaah says (interpretation of the meaning): 

“And the mosques are for Allaah (Alone), so invoke not anyone along with Allaah”

[al-Jinn 72:13] 

“And who is more astray than one who calls  on (invokes) besides Allaah, such as will not answer him till the Day of Resurrection, and who are (even) unaware of their calls (invocations) to them?”

[al-Ahqaaf 46:5] 

And the Prophet (peace and blessings of Allaah be upon him) said to Ibn ‘Abbaas (may Allaah be pleased with him): “If you ask, then ask of Allaah, and if you seek help then seek help from Allaah.” 

Narrated by al-Tirmidhi (2516) and classed as saheeh by al-Albaani in Saheeh Sunan al-Tirmidhi. 

Du’aa’ is asking for benefit and asking for harm to be warded off, and it is not only done by saying Yaa (O…), rather it has become  customary among people to use this call in du’aa’, especially when hardship comes and calamity strikes, so they say Ya Allaah, meaning O Allaah, save us, give us help, support us. 

This is the action of monotheists (believers in Tawheed) who do not call upon anyone other than Allaah. As for those who worship graves and tombs, they call upon their “saints” and revered ones, saying Ya Badawi, Ya Rifaa’i, Ya Jilaani, and what they mean is, O Badawi, help us, come to our aid, save us. 

And some of them say: Ya Rasool-Allaah, Ya Muhammad, in this manner also. This is calling upon him, seeking his help and turning to him. 

It is well known that this is one of the worst ways of going against the message that was brought by Muhammad (peace and blessings of Allaah be upon him) and the other Messengers, and that was revealed in the Books, namely the call to Tawheed and worshipping Allaah alone, and forsaking the worship of all others. 

It is not acceptable in the religion of Islam, which Allaah has chosen as the religion for His slaves, to call upon anyone except Allaah, not any Prophet who was sent or any angel who is close to Him. Rather we are to call upon Him alone. Hence Allaah says (interpretation of the meaning): 

“Is not He (better than your gods) Who responds to the distressed one, when he calls on Him, and Who removes the evil, and makes you inheritors of the earth, generations after generations? Is there any ilaah (god) with Allaah? Little is that you remember!”

[al-Naml 27:62] 

Thus it is known that if a person says Ya Muhammad or Ya Rasool Allaah, not intending thereby to call upon him and seek his help, then there is nothing wrong with it, such as if he wants to call him to mind and remember him, such as if he reads a hadeeth and says Sall-Allaah ‘alayka ya Rasool-Allaah (May Allaah send blessings upon you, O Messenger of Allaah) or How great and beautiful are your words, O Messenger of Allaah. But saying Ya Muhammad is contrary to good manners, as explained above. 

Shaykh Ibn Baaz (may Allaah have mercy on him) was asked: Is it shirk if someone says in any place on earth, Ya Muhammad Ya Rasool-Allaah, calling him? 

He replied: 

Allaah has stated in His Holy Book and on the lips of His Messenger (peace and blessings of Allaah be upon him) that worship is the right of Allaah alone and no one else has any share of it, and that du’aa’ is a kind of worship, so if a person says in any place on earth, Ya Rasool-Allaah, Ya Nabi Allaah or Ya Muhammad, help me, or save me, or support me, or heal me, or support your ummah, or heal the sick Muslims, and guide their misguided ones and so on, then he is making him a partner with Allaah in worship. The same applies to those who do the same thing with regard to other Prophets, angels, awliya’ (“saints), jinn, idols or any other created beings, because Allaah says (interpretation of the meaning): 

“And I (Allaah) created not the jinn and mankind except that they should worship Me (Alone)”

[al-Dhaariyaat 51:56] 

“O mankind! Worship your Lord (Allaah), Who created you and those who were before you so that you may become Al-Muttaqoon (the pious”

[al-Baqarah 2:21] 

End quote from Majmoo’ Fataawa al-Shaykh Ibn Baaz (2/453). 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked: Some people at times of hardship say Ya Muhammad or Ya ‘Ali or Ya Jilaani. What is the ruling on that? 

He replied: 

If the intention is to call upon them and seek their help, then the person is a mushrik in the sense of major shirk that puts one beyond the pale of Islam, and he must repent to Allaah and call upon Allaah alone, as Allaah says (interpretation of the meaning):  

“Is not He (better than your gods) Who responds to the distressed one, when he calls on Him, and Who removes the evil, and makes you inheritors of the earth, generations after generations? Is there any ilaah (god) with Allaah? Little is that you remember!”

[al-Naml 27:62] 

As well as being a mushrik, he is also fooling himself. Allaah says (interpretation of the meaning): 

“And who turns away from the religion of Ibraaheem (Abraham) (i.e. Islamic Monotheism) except him who befools himself?”

[al-Baqarah 2:130] 

“And who is more astray than one who calls on (invokes) besides Allaah, such as will not answer him till the Day of Resurrection, and who are (even) unaware of their calls (invocations) to them?”

[al-Ahqaaf 46:5] 

End quote from Fataawa al-Shaykh Ibn ‘Uthaymeen (2/133). 

And Allaah knows best.

I assume that in prayer you do not say "Assalamu Alaika Ayyuhan nabiyyu"?

If you do, according to your post, you are a Mushrik and a fool.

If you dont say that then ... what do you say?

The quote and answer you have cut and pasted also doesnt seem to give a definition of shirk because shirk is expecting help from anything outside the power of God.

If you expect it with the pwoer of God, that is not shirk, but believing that God has the power to give you help through others, just like he gave us faith through others (we did not recieve revelation, but the Prophet did, who taught his companions, who taught others who taught others...).

My belief is that if you even go to a doctor with an illness and think his medicine will cure you outside the power of God, then that is shirk. However if you believe that medicine has healing power given by the will of God, that is not shirk and that is normal and expected.

In the same way if you ask someone for help, knowing that the only one with power is God, it is not shirk and your cut and paste job is incorrect.

PS keep calling everyone kaafirs and you will be banned,