compassionate allowance can be given only in exceptional circumstances where case is found to be deserving of special consideration. The person, who has to decide, whether it is a deserving case or not, is the competent authority

2) there has to be some mitigating factor which makes the competent authority to come to the conclusion that even though the person has to be dismissed or removed from service but looking at the special mitigating circumstances, the person may be given compassionate allowance 

Yes the compassionate appointment can be given to people appointed under the scheme.

What do you mean by compassionate allowance??

Sevices are given to employees or pensionary benefits.

Compassionate appointment can be given to persons covered under the rules irrespective of whether they were appointed before or after 2004.

Provided that the authority competent to dismiss or remove him from service may, if the case is deserving of special consideration, sanction a compassionate allowance not exceeding two 'thirds of pension or gratuity or both which would have been admissible to him if he had retired on compensation pension.

There are various kinds of pension namely;

Superannuation, retirement pension, voluntary retirement, invalid pension, compensation pension, compulsory retirement pension, compassionate allowance, extra ordinary pension, family pension.

Your question falls under compassionate allowance.

Yes they are eligible for the same

It can be given to employees under new pension scheme 

Dear client,  No compassionate allowance shall be sanctioned after the expiry of the aforesaid period of six months, to a Government servant on whom a penalty of dismissal or removal from service was imposed before the date of commencement of these rules.