I am from Karachi Pakistan where almost all people are either Hanafees or barailwees (worshippers at graves). I perform prayer following the Sunnah (of the Prophet) and as the "Ahle Hadith" or "the people of Saudia" pray. People here say that it is Sunnah to do as the Imam does. Is this correct? Also, sometimes after the Imam completes al-Fatiha, I feel I must hurry and complete it before I go into Ruku. Am I right?I work in a company where I have to wear a necktie. I heard that wearing a tie is a sign of Christians? What should I do?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

You should imitate your Imam in not performing the Sunan (not obligatory acts) if your performing such Sunan independently could in any way affect your following the Imam in all prayer acts.
Know that the Hadith of following the Imam is sound and should then be applied strictly. So, anything that could cause a person to cease following the Imam, to precede him or not to remain behind him, should be avoided as it is unlawful. But the Sunan which, if done, do not affect the imitation of the Imam could be performed. For example, if the Imam does not raise his hands while performing Takbeer when standing up from Ruku, one can raise his hands.
As for the Fatiha, it is a Rukn (Integral) of the prayer. The prayer can not accepted without it. It is obligatory on the Imam and on those praying behind him. This is the preponderant opinion of scholars according to these Ahadith of the Prophet.
Ubadah Bin Saamit reported that the Prophet said: "Whoever does not recite Al-Fatiha in his prayer, his prayer is invalid". [Reported by Imam Bukhari and Imam Muslim].
The Prophet also said: "Pray as you have seen me praying". [Reported by Imam Bukhari and Imam Muslim].
The person who follows an Imam should recite the Sura-al-Fatiha when the Imam pauses (keeps quiet). An Imam has two pauses. Abu Salama Bin Abdur Rahman said: 'Every Imam has two pauses you should use them to recite Sura-al-Fatiha; the one when he enters and the second when he finishes reciting Sura-al-Fatiha'. If an Imam does not have pause you may recite it when he recites it.

3. The necktie originated in Europe. It is said that it was a symbol for the obedience of the husband to his wife. Then it became what it is now. Wearing has become a habit for many Muslims and is no longer a tradition just for non-believers. If the believer wears it only to imitate the westerners, reference to it is included in the sound Hadeeth "Whoever imitates a people, he is one of them". So it is safer for the Muslim to avoid wearing it unless this could cause him some harm, such as being fired from his job. So, if not wearing a tie might cause you harm at work, you can wear it.
Allah knows best.