Whether all decisions and orders can be appealed

No. in terms of Section 121, orders listed below cannot be appeal against:
(a) An order of the Commissioner or other competent authority for transfer of proceeding from one officer to another officer; or
(b) an order pertaining to the seizure or retention of books of account, register and other documents; or
(c) an order sanctioning prosecution under this Act; or
(d) an order passed under section 80 relating to payment of tax, interest and other dues in installments.

(ICAI FAQ PUBLICATIONS 06-09-2017 Non appealable decision and orders : FAQ NO.64)

Whether amounts confirmed in terms of the order of Tribunal / High Court to be remitted even though appeal is preferred before High Court or Supreme Court

Yes. Notwithstanding that an appeal has been preferred to the High Court or the Supreme Court, sums due to the Government as a result of an order passed by the Tribunal or an order passed by the High Court, as the case may be, shall be payable in accordance with the order so passed.

(ICAI FAQ PUBLICATIONS 06-09-2017 Sums due to be paid notwithstanding appeal, etc. : FAQ NO. 63)

What are the orders against which appeal could be preferred before the Supreme Court

Following orders could be challenged before the Supreme Court:
(a) Order passed by the National Bench or Regional Benches of the Appellate Tribunal; or
(b) Judgment or order passed by the High Court in an appeal made under section 117 in any case which, on its own motion or on an application made by or on behalf of the party aggrieved, immediately after passing of the judgment or order, the High Court certifies to be a fit one for appeal to the Supreme Court.

(ICAI FAQ PUBLICATIONS 06-09-2017 APPEALS TO SUPREME COURT:  FAQ NO. 62)

Whether the appeal could be decided by a judge sitting singly

No. Appeal filed before the High Court, shall be heard by a bench of not less than two Judges of the High Court, and shall be decided in accordance with the opinion of such Judges or of the majority, if any, of such Judges.
Where there is no such majority, the Judges shall state the point of law upon which they differ and the case shall, then, be heard upon that point only, by one or more of the other Judges of the High Court and such point shall be decided according to the opinion of the majority of the Judges who have heard the case including those who first heard it.

(ICAI FAQ PUBLICATIONS 06-09-2017 APPEALS TO HIGH COURT: FAQ NO. 61)

Who could represent before GST officer of Appellate Authority or the Tribunal

Following persons could act an authorized representative and appeal before the officer or Appellate Authority or the Hon’ble Tribunal on behalf of an assessee
(a) relative or regular employee of the assessee; or
(b) an advocate who is entitled to practice in any court in India, and who has not been debarred from practicing before any court in India; or
(c) any chartered accountant, a cost accountant or a company secretary, who holds a certificate of practice and who has not been debarred from practice; or
(d) a retired officer of the Commercial Tax Department of any State Government or Union territory or of the Board who, during his service under the Government, had worked in a post not below the rank than that of a Group-B Gazetted officer for a period of not less than two years. However, such officer shall not be entitled to appear before any proceedings under this Act for a period of one year from the date of his retirement or
resignation; or
(e) any person who has been authorised to act as a goods and services tax
practitioner on behalf of the concerned registered person.
Following shall not be entitled to appear:
(a) who has been dismissed or removed from Government service; or
(b) who is convicted of an offence connected with any proceedings under this Act, the State Goods and Services Tax Act, the Integrated Goods and Services Tax Act or the Union Territory Goods and Services Tax Act, or under the old law or under any of the Acts passed by a State Legislature dealing with the imposition of taxes on sale of goods or supply of goods or services or both; or
(c) who is found guilty of misconduct by the prescribed authority;
(d) who has been adjudged as an insolvent, during the period in which he is
insolvent.

(ICAI FAQ PUBLICATIONS 06-09-2017 ORDERS OF APPELLATE TRIBUNAL: FAQ NO. 55)