Whether penalty is imposable for supply of goods or services without issue of any invoice or when an incorrect or false invoice is issued with regard to such supply

Yes, in terms of Section 122(1)(i) of the CGST Act, 2017 the above supply of goods and services will be considered to be offence attracting penalty of ten thousand rupees or an amount equivalent to the tax evaded, whichever is higher.

(ICAI FAQ PUBLICATIONS 06-09-2017 Penalty for certain offences: FAQ NO. 1)

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)