"the Twelve have no right to go into Zion, or any of her stakes, and there undertake to regulate the affairs thereof, where there is a standing high council; but it is their duty to go abroad and regulate all matters relative to the different branches of the Church. When the Twelve are together, or a quorum of them, in any church, they will have authority to act independently , and make decisions, and those decisions will be valid. But where there is not a quorum, they will have to do business by the voice of the Church. No standing high council has authority to go into the churches abroad and regulate the matters thereof, for this belongs to the Twelve. No standing High Council will ever be established only in Zion, or one of her stakes. When the Twelve pass a decision, it is in the name of the Church, therefore it is valid."

(I'm a bit uncertain as to what all of this means precisely. Initially it seems that the Twelve are unable to regulate wards and stakes, but only branches, but continuing on it appears that when they are together, they can do anything administratively, but that when they are not, then not even branches can be regulated without appealing to the voice of the Church. This "Church" seems to be the whole church as an organization. Perhaps then it is intended to mean that when they are together, they have power to act independently because they can speak for the Church, but when they are apart, they have no such power and must act according to policy already voiced and decisions already made, perhaps including those being made by the first presidency. What I can't explain beyond this is how their authority differs in stakes/wards and in districts/branches. Perhaps we are to understand that they only act as the voice of the church within the sphere of districts/branches since this is the only sphere in which they have regulatory authority, and hence the first stament confines how we are to understand "the Church", or confines the scope of the pronouncements that can be made on behalf of "the Church".)

Since the Twelve and the Seventy are called to be traveling ministers, they have to depend upon their ministry for support and have a unique right to call upon the churches for their support, and the support of their families.

Presidents of the seventy serve at the call of the Twelve.

"...the Twelve are not subject to any other than the First Presidency..."

The Apostles are prophets, seers, and revelators.
The Apostles are called to go forth and preach the Gospel. It is not required for them to go two by two, as at former times.

"... the Twelve ... have the keys of the ministry."

Strengthen the Bond of Brotherhood among All Quorum Members
Learn Fundamental Doctrines and Priesthood Duties
Fulfill Service Assignments Involving the Entire Quorum

"The strength of a quorum comes in large measure from how completely its members are united in righteousness."

The 12 Apostles are not accountable to the High Council, but only "to the General Council of the authorities of the whole Church, according to the revelations."