Does there have to be one imaam and does he have to be the khateeb?

Praise be to Allah.

1- If the mosque can be taken care of by one imaam, and is not one of the large mosques that need the cooperation of more than one imaam, or there is a person who can work full-time as an imaam and you have the financial resources to meet his needs (i.e., pay him a salary), or there is someone who can do this voluntarily, then appointing one imaam and khateeb for the mosque will bring a number of benefits, such as:

(i) A regular khateeb will be more able to get to know the problems faced by the people, and thus will be able to play a part in solving them. He will be a point of reference and a leader for the people of the mosque. If the people know that he will be coming back again, this will encourage them to discuss issues and problems with him. 
(ii) People will be able to listen to useful things that need to be spoken about in a series of khutbahs, e.g., the tafseer of Soorat al-Faatihah, or the Signs of the Hour, or the battles (of the Prophet (peace and blessings of Allaah be upon him)), or teaching the salaah (prayer). Such series can usually only be done by one imaam, which is not the case when the khateeb is different each week. 
(iii) The people will be able to listen to something new each week, because a regular khateeb will not repeat the same topics too soon, lest he bore the people. He will come up with something new each week, unlike what happens with different imaams who tell the people similar things time and time again, which wastes time that otherwise could be put to good use.
(iv) If the khateeb is also the imaam, this is better, because he will know all the matters and problems concerning the people of the mosque. Things may happen during the week to the people of the neighbourhood or those who attend the mosque, which requires the comments of the imaam, or he may refer to them in the Jumu'ah khutbah.
(v) This is also in accordance with the teaching of the Prophet (peace and blessings of Allaah be upon him) and the khaleefahs who succeeded him, where the imaam and regular khateeb were one and the same.

2. You must be very careful to make sure that the imaam is one of the Ahl al-Sunnah and that he follows their 'aqeedah. This is what will benefit you in your religion; anyone else who is a follower of bid'ah will only cause you harm and lead you astray.

3. In addition to his having a sound 'aqeedah, he must also be knowledgeable, so that you will hear something useful in his lessons and khutbahs.

4. There is no reason why you should not form a committee, including some knowledgeable brothers, to choose an imaam and khateeb, because people's emotions may prevent them from distinguishing between what is beneficial and what is harmful (i.e., they may not make the right choice of imaam). 

5. It is not essential for the person to be able to be both imaam and khateeb. Many famous qaari's (readers of Qur'aan) know nothing about the rulings of sharee'ah, and many eloquent khateebs are unsure of the rulings on sujood al-sahw (prostration of forgetfulness), and many knowledgeable people cannot give khutbahs and address the people.

If it is necessary to have an imaam who is different from the khateeb, there is nothing wrong with that. If the circumstances of the community do not permit one person to be a full-time imaam and khateeb because of study and work commitments, then it is OK to appoint a group of people who are qualified to act as imaams and khateebs, and to draw up a roster so that the mosque will be able to fulfil its responsibilities and not falter in its work. We ask Allaah to help us and you to do that which is good. May Allaah bless our Prophet Muhammad.