Who would appoint the President and Members

The President and the Judicial Members of the National Bench and the Regional Benches shall be appointed by the Government after consultation with the Chief Justice of India or his nominee.
The Technical Member (Centre) and Technical Member (State) of the National Bench and Regional Benches shall be appointed by the Government on the recommendations of a Selection Committee consisting of such persons and in such manner as may be prescribed. The Judicial Member of the State Bench or Area Benches shall be appointed by the State Government after consultation with the Chief Justice of the High Court of the State or his nominee
The Technical Member (Centre) of the State Bench or Area Benches shall be appointed by the Central Government and Technical Member (State) of the State Bench or Area Benches shall be appointed by the State Government in such manner as may be prescribed.

(ICAI FAQ PUBLICATIONS 06-09-2017 Qualification, appointment & condition of service of the President and the members of the Tribunal: FAQ NO. 34)

What is the qualification to be appointed as Member (Technical)

Member Technical (Centre): A person shall not be qualified for appointment as a Member Technical (Centre), unless he is or has been a member of Indian Revenue (Customs and Central Excise) Service, Group A, and has completed at least fifteen years of service in Group A;
Member Technical (State) : A person shall not be qualified for appointment as a
Technical Member (State) unless he is or has been an officer of the State Government not below the rank of Additional Commissioner of Value Added Tax or the State goods and services tax or such rank as may be notified by the concerned State Government on the recommendations of the Council with at least three years of experience in the administration of an old law or the State Goods and Services Tax Act or in the field of finance and taxation.

(ICAI FAQ PUBLICATIONS 06-09-2017 Qualification, appointment & condition of service of the President and the members of the Tribunal: FAQ NO. 33)

What is the qualification to be appointed as Judicial Member

A person shall not be qualified for appointment as a Judicial Member, unless:
(i) He has been a Judge of the High Court; or
(ii) Is or has been a District Judge qualified to be appointed as a Judge of a High Court; or
(iii) Is or has been a Member of Indian Legal Service and has held a post not less than Additional Secretary for three years.

(ICAI FAQ PUBLICATIONS 06-09-2017 Qualification, appointment & condition of service of the President and the members of the Tribunal: FAQ NO. 32)

What is the qualification to be appointed as President?

A person shall not be qualified for appointment as President unless:
(a) He has been a Judge of the Supreme Court or
(b) He is or has been the Chief Justice of a High Court, or
(c) He is or has been a Judge of a High Court for a period not less than five years;

(ICAI FAQ PUBLICATIONS 06-09-2017 Qualification, appointment & condition of service of the President and the members of the Tribunal: FAQ NO. 31)

Whether members of the Tribunal could be transferred from one bench to other bench

Central Government in consultation with the President, may transfer Judicial Member or a Member Technical (State) from National Bench or one Regional Bench to other Regional Bench or to National Bench. Further, Member Technical (Centre) could be transferred from one Bench to another Bench, whether National, Regional, State or Area. However, State Government could transfer member technical (state) from State Bench or one area bench to another area bench or to State Bench.

(ICAI FAQ PUBLICATIONS 06-09-2017 Constitution of Appellate Tribunal: FAQ NO. 30)

What would be consequence where there is a difference of opinion on any issue among the members of the bench

If the Members of the Bench (National/Regional/State/Area) differ in opinion on any point or points, it shall be decided according to the opinion of the majority, if there is a majority, but if the Members are equally divided, they shall state the point or points on which they differ, and the case shall be referred by the President or as the case may be, State President for hearing on such point or points to one or more of the other Members of the National Bench, Regional Benches, State Bench or Area Benches and such point or points shall be decided according to the opinion of the majority of Members who have heard the case, including those who first heard it.

(ICAI FAQ PUBLICATIONS 06-09-2017 Constitution of Appellate Tribunal: FAQ NO. 29)

Whether any matter could be heard by bench consisting of members less than 3 as set out above

Yes, in the absence of a Member in any Bench due to vacancy or otherwise, any appeal may, with the approval of the President or, as the case may be, the State President, be heard by a Bench of two Members. Further, where the tax or input tax credit involved or the difference in tax or input tax credit involved or the amount of fine, fee or penalty determined in any order appealed against, does not exceed ` 5 Lakhs and which does not involve any question of law may, with the approval of the President and subject to such conditions as may be prescribed on the recommendations of the Council, be heard by a bench consisting of a single member.

(ICAI FAQ PUBLICATIONS 06-09-2017 Constitution of Appellate Tribunal: FAQ NO. 28)

What is the composition of State Bench and Area Benches

Each State Bench and Area Benches shall consist of a Judicial Member, one Technical Member (Centre) and one Technical Member (State) and the State Government may designate the senior most Judicial Member in a State as the State President.

(ICAI FAQ PUBLICATIONS 06-09-2017 Constitution of Appellate Tribunal: FAQ NO. 27)

What is jurisdiction of State Bench or Area Bench

State Bench or Area Benches shall have jurisdiction to hear appeals against the orders passed by the Appellate Authority or the Revisional Authority in the cases involving matters other than those involving dispute relating to place of supply

(ICAI FAQ PUBLICATIONS 06-09-2017 Constitution of Appellate Tribunal: FAQ NO. 26)

What is State Bench or Area Bench

The Government, by notification, specify for each State or Union territory, a Bench of the Appellate Tribunal, exercising the powers of the Appellate Tribunal within the concerned State or Union territory.
Government shall, on receipt of a request from any State Government, constitute such number of Area Benches in that State, as may be recommended by the Council

(ICAI FAQ PUBLICATIONS 06-09-2017 Constitution of Appellate Tribunal: FAQ NO. 25)