Assalaamu alaikum warehmatullahi wabarakatuhu brother,
First of, you wanting to serve your country and CASE 1:-
"Fight in the cause of Allah those who fight you, but do not transgress limits; for Allah loveth not transgressors." (Quran 2:190)
And fight them until there is no more afflictions (i.e. no more worshipping of others besides Allah). " (2.193) Ibn 'Umar said (to the man), "Do you know what is meant by afflictions? Let your mother bereave you! Muhammad used to fight against the pagans, for a Muslim was put to trial in his religion (The pagans will either kill him or chain him as a captive) . His fighting was not like your fighting which is carried on for the sake of ruling."
Volume 4, Book 52, Number 46 :
Narrated by Abu Huraira
I heard Allah's Apostle saying, "The example of a Mujahid in Allah's Cause-- and Allah knows better who really strives in His Cause----is like a person who fasts and prays continuously. Allah guarantees that He will admit the Mujahid in His Cause into Paradise if he is killed, otherwise He will return him to his home safely with rewards and war booty."
Volume 4, Book 52, Number 42 :
Narrated by Ibn 'Abbas
Allah's Apostle said, "There is no Hijra (i.e. migration) (from Mecca to Medina) after the Conquest (of Mecca), but Jihad and good intention remain; and if you are called (by the Muslim ruler) for fighting, go forth immediately.
Conclusion: The meaning of Jihad is to fight (with the intention to be sacrificed) in Allah's cause. The country's purpose is to mainly conquer the land or protect their land mostly but it is not their intentions, if the country states that it is in Allah's cause then it is jihad!
IN CASE 2:-
"And if two parties of the believers quarrel, make peace between them; but if one of them acts wrongfully towards the other, fight that which acts wrongfully until it returns to Allah's command; then if it returns, make peace between them with justice and act equitably; surely Allah loves those who act equitably.(49.9)
Volume 3, Book 43, Number 622 :
Narrated by 'Abdullah bin Umar
Allah's Apostle said, "A Muslim is a brother of another Muslim, so he should not oppress him, nor should he hand him over to an oppressor. Whoever fulfilled the needs of his brother, Allah will fulfill his needs; whoever brought his (Muslim) brother out of a discomfort, Allah will bring him out of the discomforts of the Day of Resurrection, and whoever screened a Muslim, Allah will screen him on the Day of Resurrection . "
Conclusion: A muslim country or brother can not fight eachother as they are (in Islam/muslim) brothers to eachother.
IN CASE 3:-
Volume 4, Book 52, Number 63 :
Narrated by Al-Bara
A man whose face was covered with an iron mask (i.e. clad in armor) came to the Prophet and said, "O Allah's Apostle! Shall I fight or embrace Islam first? "The Prophet said, "Embrace Islam first and then fight." So he embraced Islam, and was martyred. Allah's Apostle said, A Little work, but a great reward. "(He did very little (after embracing Islam), but he will be rewarded in abundance)."
Conclusion:- Jihad is done in Allah's cause therefore one needs to be Muslim (believe in Allah, his messengers, Angels, revelations, signs etc)
Volume 4, Book 52, Number 50 :
Narrated by Anas bin Malik
The Prophet said, "A single endeavor (of fighting) in Allah's Cause in the forenoon or in the afternoon is better than the world and whatever is in it."
Volume 4, Book 52, Number 41 :
Narrated by Abdullah bin Masud
I asked Allah's Apostle, "O Allah's Apostle! What is the best deed?" He replied, "To offer the prayers at their early stated fixed times." I asked, "What is next in goodness?" He replied, "To be good and dutiful to your parents." I further asked, what is next in goodness?" He replied, "To participate in Jihad in Allah's Cause." I did not ask Allah's Apostle anymore and if I had asked him more, he would have told me more.
Volume 4, Book 52, Number 59 :
Narrated by Abu Huraira
Allah's Apostle said, "By Him in Whose Hands my soul is! Whoever is wounded in Allah's Cause....and Allah knows well who gets wounded in His Cause....will come on the Day of Resurrection with his wound having the color of blood but the scent of musk."