Sir,
The question posted by you,"Does Islam really order Muslims to not take Jews, Christians and other non-Muslims as friends?" in view of verse 5:51 can be easily answered.
Arabic original version of the verse is,
[005:051] Ya ayyuha allatheena amanoo la tattakhithoo alyahooda waalnnasara awliyaa baAAduhum awliyao baAAdin waman yatawallahum minkum fa-innahu minhum inna Allaha la yahdee alqawma alththalimeena
Its translation as per given by you are
[005:051] O ye who believe! take not the Jews and the Christians for your friends and protectors: They are but friends and protectors to each other. And he amongst you that turns to them (for friendship) is of them. Verily God guideth not a people unjust.
-Translation from the book by Yousuf Ali.
Similar such verses in Holy Quran which can misguide when quoted out of contextare
"O ye who believe! Take not for friends and protectors those who take your religion for a mockery or sport - whether among those who received the Scripture (i.e., the Bible) before you, or among those who reject Faith; but fear ye Allah, if ye have Faith (indeed). (The Noble Quran, 5:57)"
"Yea, to those who take for friends unbelievers rather than believers: is it honour they seek among them? Nay,- all honour is with God. (The Noble Quran, 4:139)"
"O ye who believe! Turn not (for friendship) To people on whom Is the Wrath of Allah. Of the Hereafter they are Already in despair, just as The Unbelievers are In despair about those (Buried) in graves. (The Noble Quran, 60:13)"
In the above Noble Verses, the Arabic word for "friends" is "Awliyaa", which has four literal meanings: (1) Allies; (2) Friends; and (3) Guardians. In Noble Verse 60:13, the Arabic word used was "tatawallu", which is derived from the root word "Awliyaa".
"Waliy" which is the singular of "Awliyaa" means "Guardian" as your parents were your guardians when you were a kid. So as you can see, the Arabic word "Awliyaa" has different literal meanings.
Important Note: In Noble Verse 60:13 above, Allah Almighty said "la tatawallu qawman", which literally means "take not as allies a tribe (or a community)", which further proves my point that "Awliyaa" in the Noble Verses above is meant for "alliance" and not personal "friendship".
*** There is nothing wrong with developing a personal friendship with a non-Muslim to help him/her understand and appreciate Islam and to ultimately embrace it if they chose to. As clearly shown in the introduction above, Allah Almighty commanded all Muslims to treat with kindness and justice all of the good non-Muslims.
The English translation of the Noble Verses above is not accurate, because the use of the word "friends" is really out of context. The word "Allies" is the correct one, because in all of the Noble Verses above Allah Almighty was talking to the Muslims as a group taking A GROUP OF PEOPLE OR COMMUNITY as "Awliyaa", which fits perfectly with "alliance" than with just personal "friendship" on an individual level.
Another example of inaccurate English translation is the following Noble Verse:
"As to those who turn (For friendship) to Allah, His Messenger, and the (Fellowship of) Believers - it is the Fellowship of Allah that must certainly triumph. (The Noble Quran, 5:56)"
The Arabic word for "Fellowship" of Allah is "hizb", which literally mean "Alliance", as in "Hizbullah" in Lebanon, which means "The Alliance of Allah". Hizbullah are the guerrillas and the warriors that fought the Israelis long battles in southern Lebanon and finally were able to drive them out. Also, the "Northern Alliance" in Afghanistan against the Taliban are called "Hizb Al-shamal".
Hizb is mistranslated as "Fellowship" instead of "Alliance". Noble Verse 5:56 clearly states that Muslims must form their alliances only with Allah Almighty, Prophet Muhammad and the Believers. Any alliance other than Allah Almighty is a losing one. That is exactly what the Alliance with the Jews, Christians and Pagans against fellow Muslims will result in: Eventual loss at this life, and Severe Punishment at the Day of Judgement.
So the Noble Verses above don't suggest that Muslims can not have personal friends with non-Muslims. It suggests that Muslim countries are prohibited from forming alliance with the non-Muslims against other Muslims.
Noble 5:57, however, clearly states that Muslims should avoid having personal friendship with anyone (Muslim or non-Muslim) who disrespects Islam and take it for a "mockery". So the translation of "friends" for "Awliyaa" seem to be a correct and accurate one.
The use of the word "friends" for Noble Verses 5:51 and 4:139 as a translation is ambiguous. It is not clear from the Noble Verses that Allah Almighty meant for "Awliyaa" to be only personal "friends". Certainly Noble Verse 5:56 above clearly shows that Allah Almighty is concerned about the Alliance that Muslims commit themselves to, and not personal friendships.
Verse 9:5 can be answered more easily if you look at succeeding verse,
The original Arabic version is,
[009:005] Fa-itha insalakha al-ashhuru alhurumu faoqtuloo almushrikeena haythu wajadtumoohum wakhuthoohum waohsuroohum waoqAAudoo lahum kulla marsadin fa-in taboo waaqamoo alssalata waatawoo alzzakata fakhalloo sabeelahum inna Allaha ghafoorun raheemun
[009:006] Wa-in ahadun mina almushrikeena istajaraka faajirhu hatta yasmaAAa kalama Allahi thumma ablighhu ma/manahu thalika bi-annahum qawmun la yaAAlamoona
Quoting Yusuf Ali's translation as per your request(I believe you have his translation book,but you will also require a "book on Tafsir (elaborations/details)"to understand the ambigous Arabic words which has no/faulty English equivalent or tends to give more than one meaning)
[009:005] But when the forbidden months are past, then fight and slay the Pagans wherever ye find them, an seize them, beleaguer them, and lie in wait for them in every stratagem (of war); but if they repent, and establish regular prayers and practise regular charity, then open the way for them: for God is Oft-Forgiving, Most Merciful.
[009:006] If one amongst the Pagans ask thee for asylum, grant it to him, so that he may hear the word of God; and then escort him to where he can be secure. That is because they are men without knowledge.
Allah Almighty certainly DOES NOT ask every non-muslim to be slain which would appear so if you quote Verse 9:5 only without the succeeding verse.
Yours Truly,
Tabrez Zakaria