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)

Where an assessee gets a favourable decision either before Appellate Authority or the Tribunal, whether the pre-deposit would be refunded back? Whether any interest is paid

Yes, where the assessee gets a favourable decision (fully or partially), the amount paid as pre-deposit would be refunded along with interest which is computed from the date of deposit till date of refund.
Further, Section 115 provides that interest at the rate specified under section 56 shall be payable in respect of such refund from the date of payment of the amount till the date of refund of such amount.

(ICAI FAQ PUBLICATIONS 06-09-2017 ORDERS OF APPELLATE TRIBUNAL: FAQ NO. 54)

Whether Tribunal has power to rectify / amend the orders passed by it

Yes, Tribunal may amend any order passed by it under in terms of Section 113(1) so as to rectify any mistake apparent from the record. Tribunal could undertake rectification on its own or on application by either of the parties to the appeal. The application for rectification shall be made within a period of three months from the date of the order sought to be rectified.
However, no amendment which has the effect of enhancing an assessment or reducing a refund or input tax credit or otherwise increasing the liability of the other party, shall be made under this sub-section, unless the Tribunal has given notice to him of its intention to do so and has allowed him a reasonable opportunity of being heard.

(ICAI FAQ PUBLICATIONS 06-09-2017 ORDERS OF APPELLATE TRIBUNAL: FAQ NO. 53)

What are the orders that could be passed by the Appellate Tribunal

The Hon’ble Tribunal may pass such orders thereon as it thinks fit, confirming, modifying or annulling the decision or order appealed against or may refer the case back to the Appellate Authority, or the Revisional Authority or to the original adjudicating authority, with such directions as it may think fit, for a fresh adjudication or decision after taking additional evidence, if necessary.

(ICAI FAQ PUBLICATIONS 06-09-2017 ORDERS OF APPELLATE TRIBUNAL: FAQ NO. 52)

Whether the parties to an appeal could seek adjournment of the hearing

The Tribunal may, if sufficient cause is shown at any stage of hearing of an appeal, grant time, from time to time, to the parties or any of them and adjourn the hearing of the appeal for reasons to be recorded in writing. However, no such adjournment shall be granted more than three times to a party during hearing of the appeal.

(ICAI FAQ PUBLICATIONS 06-09-2017 Orders of Appellate Tribunal: FAQ NO. 51)