About the question regarding Imamate.
We see in a famous Hadith Qudsi from Imam Ridha (as) that on his way to Neysabour when the people asked the Imam for advice as his caravan was leaving. He said “The statement, there is no god but Allah is my fortress. Whoever enters my fortress will be saved.” Then the Imam turned and said “With its conditions and I am one of its conditions.”
From this we see that belief in the Imam is essential to complete the belief in Tawhid and without it one belief in Tawhid will remain incomplete.
One may ask how is this possible? Once the belief in One God is established, we must believe that He is just and due to His being just He will inform us of Himself. He does this by sending us messengers to guide us, after the messenger dies then He must have people to safeguard this message of Islam, so He appoints Imams for us.
Also, this links to Me’ad (return on the day of judgement), Allah says
يَوْمَ نَدْعُو كُلَّ أُنَاسٍ بِإِمَامِهِمْ ۖ فَمَنْ أُوتِيَ كِتَابَهُ بِيَمِينِهِ فَأُولَٰئِكَ يَقْرَءُونَ كِتَابَهُمْ وَلَا يُظْلَمُونَ فَتِيلًا
“(Remember) the day when We will call every people with their Imam; then whoever is given his book in his right hand, these shall read their book; and they shall not be dealt with a whit unjustly.” Quran 17:71
He also states that He will bring a witness from every nation and bring the prophet as a witness over them.
“How will it be, then, when We bring from every people a witness and bring you as a witness above these” Quran 4:41
We see that in Tafir al-Ayashi there is a narration from Imam Baqir (as) about this verse that the witness from every nation is it’s Hujjah (proof) which are the prophets and their successors and the witness above these proofs is the Holy Prophet (s).
Imam Sadiq (a.s) was asked about the meaning of the above Quranic verse which he replied, 'This verse refers particularly to the nation of the Holy Prophet (s) In every era an Imam from among us is a witness upon them and the Holy Prophet (s) is a witness upon us.' 
This is one of the ways that believing in the Imam of our time is linked to the belief in the Oneness of God.
We find in Ilal Shari by Sheikh Saduq a beautiful narration by the Prophet (s): “The stars are a security for the inhabitants of the sky, and the People of my Household are a security for the inhabitants of the earth. So, if the stars were to go away, there would come to the inhabitants of the sky what they dislike, and if the People of my Household go away, there would come to the inhabitants of the earth what they dislike’ – meaning by the People of the Household, the Imams, the obedience to whom Allah has Paired as being obedience to Him, so He Said [4:59] O you who believe! Obey Allah and obey the messenger and those in authority from among you, and they are the Infallible, the Purified who are not committing any sins nor are they disobeying (Allah), and they are the supporters, the conciliators, the Guides due to whom Allah sustains His servants. It is due to them that His Countries survive, and it is due to them that there are drops (of rain) from the sky, and it is due to them that the Blessings come out from the earth, and it is due to them that the Torment and the Punishment is delayed and is not hastened upon the people of the disobedience. Neither will the Holy Spirit separate from them nor would they separate from it. Neither will they separate from the Quran; nor would it separate from them”
We see that Allah commands us to obey the Prophet and those who possess the authority (Imams) unconditionally and their obedience is linked to the obedience of Allah (swt).
يَا أَيُّهَا الَّذِينَ آمَنُوا أَطِيعُوا اللَّهَ وَأَطِيعُوا الرَّسُولَ وَأُولِي الْأَمْرِ مِنكُمْ ۖ فَإِن تَنَازَعْتُمْ فِي شَيْءٍ فَرُدُّوهُ إِلَى اللَّهِ وَالرَّسُولِ إِن كُنتُمْ تُؤْمِنُونَ بِاللَّهِ وَالْيَوْمِ الْآخِرِ ۚ ذَٰلِكَ خَيْرٌ وَأَحْسَنُ تَأْوِيلًا
“O you who believe! obey Allah and obey the Messenger and those in authority from among you; then if you quarrel about anything, refer it to Allah and the Messenger, if you believe in Allah and the last day; this is better and very good in the end.” Quran 4:59
This absolute obedience that Allah commands us to follow them in is without any conditions, meaning that they must be infallible because Allah would never command us to obey someone in sins or mistakes. We see that other places in the Quran where Allah has commanded us to follow fallible beings such as our parents, but the obedience was not absolute, rather it was limited with the condition that they do not command you to obey them in worshipping other than Allah or wrongdoing.
 Ilal Shari by Sheikh Saduq Chapter 103
 Al-Kafi, vol. 1, p.190, tradition 1
There are numerous verses about Imamate in Quran. I suggest you to read the book Peshawar Nights and this will show you numerous evidences even from the Sunni's text.