Let them process your relieving, you can join the bank. Don`t disclose anything until not asked either to resigning bank nor to joining bank otherwise they will create useless restrain and will demand NOC.

We do not advice you to suppress material facts 

disclose that you wrre were employed in govt job and that you had resigned 

See if they find out then it can create problem it would be better to seek NOC and disclose same before joining.

Company can not legally hold you once you submitted resignation letter for good reasons.so no need to bother for reliving order. Join new company. You can disclose all relevant facts about your previous job to new employer. Keep acknowledgements of your resignation letter with you for some times say 2/3 months. 

Dear Client

If you doesn't disclose your current employment to bank it can cause trouble if you doesn't get relieving letter from present employer in time because it can be termed as double employment.

But you can join bank by disclosing about current employer and submitting a copy of Resigning letter you have given in that Department so that your last working day is before joining date of bank can be confirmed by the bank.

You are not advised to suppress facts but didn't disclose till they ask,

join the new job, don't disclose anything until they ask for the same.

No it will not.  You can still file a complaint with office of labour commissioner for the same

Not only will you lose your govt job, but also you're liable to be prosecuted.. 

No, this is up to you to show or not to show any experience if you think it is not relevant and has not been required except any criminal proceedings details if pending in department or in any court of law in India.

If it was a temporary employment and since you have applied for the present job when you were not employed, then you may not disclose the previous employment because you are not going to claim experience or any other benefits out of that employment with the new employer.