Is denying time to challenge 10 day old order a violation of fundamental right?

NO. 

It is usually not considered a violation of your fundamental right. 

You are expected to pursue appropriate legal remedies. 

If you are aggrieved by the order passed in an IA, the appropriate remedy is to file a Civil Revision Petition under Article 227 of the Constitution of India. This is a common practice in some states of India. 

You can file a Civil Revision Petition to set aside the order passed in the IA. You can also file a stay petition within the Civil Revision Petition to stay further proceedings or to stay the operation of the order. 

A Writ Petition is usually not encouraged against other courts. But in some states of India, a Writ Petition against another court is accepted. You need to find out the normal practice in your state. 

A Writ Petition is the last option, if you do not have any other option. 

A Civil Revision Petition is a better option, if it is the normal practice in your state. 

Whatever petition you want to file to challenge the order, you go ahead and prepare the petition. If you do not have enough time to prepare a perfect final petition, you prepare at least a rough draft of the petition and the other things you want to file along with the petition. 

As soon as you file a petition, they will give you a temporary number known as the SR number or Filing number. 

Then, you file a memo informing the court that you filed a petition in the higher court and you also give the SR number and the date of filing. The court will be compelled to give you a few days' time. But the court will not wait indefinitely. 

Meanwhile, you fix any defects in your petition and bring it to final perfect form and get a hearing in the court. You can also request for an urgent hearing. 

Usually we also file a stay petition along with the challenging petition. Get the stay order and file it in the lower court. You have to request them to give you the stay order copy quickly. Usually they upload it on the website and it may be sufficient. 

After you get a stay order from the higher court, the lower court is bound to wait. You may have to renew it periodically. Otherwise it may expire. 

You must act quickly. The lower court is not bound to give you sufficient time. Some judges are good. Some are not good. They are also under pressure from your opponents. 

There is also a danger of your challenging petition becoming INFRUCTUOUS. If the lower court passes any subsequent order or does any such thing, your challenging petition may become INFRUCTUOUS. Please ask your lawyer about it because it depends on the actual proceedings in the suit. 

Before filing the challenging petition and before getting a SR number, the lower court is not bound by your request memo. Even after getting the SR number, you will get only a few days' time. The only way is to get an urgent hearing and a stay order from the higher court. 

Filing a memo requesting time, without a SR number, is not a correct step. 

Dear Sir, is it a question of limitation or jurisdiction. Limitation means specific time frame to file a suit, if your suit is within a time frame, and it is dismissed, then you can file a revision petition or approach high court under Art 227 of constitution, if your suit is in wrong court i.e it is not the court authorised to hear the suit, please find out and file in an appropriate one.

Secondly, if your suit does not disclose cause of action i.e., the basis for which suit is filed, e.g., Mr. A wants to file a suit for ownership and possession against Mr.B, and is saying that Mr.A executed a sale deed, during suit, it is found out that property does not belong to Mr.A  Mr. B's suit will be dismissed for the want of cause of action. Thank you.

There's no limitation for filing of a civil revision petition before high court against the orders in IA passed by the trial court.

Since the trial court is not entertaining your memo to adjourn the case till you are filing the revision petition, you don't delay any further and file the same immediately along with a stay petition to stay the proceedings of the trial court till the disposal of the civil revision petition before high court.

That is Appropriate Course of Action.

Did you/  your lawyer move to High Court assailing the order passed by Trail Court ?

Certainly, a pettion under Article 227 lies to the High Court.