GST: Multi-state

Company is into services business. It has excess IGST credit available in MP and no credit available in Bihar. So, is there any restriction (under GST Act) of not issuing invoice from one state to another state?

There may be query but point is company having multiple registration in multi-states are not restricted to issue invoices from one state to another state evenif they have local registration, isn't it? Or my assumption is incorrect?

I didn't find any specific restriction where it is not allowed

Services definition is not limited to renting of property. Services are of wide scope. It can either be professional, technical, consultancy, construction, and so on. 

Agreed. Return are not filed on All India Basis. However, if an entity has multiple registrations, is there any restriction anywhere in GST Act that they have to first supply from the state registration and then only from other state ?

One another example:

 Manufacturing Company having registration in say 10 states. If say in a month, due to scarcity (or any other reason) of material they were unable to manufacture in particular State X. Now they have material available in State Y. Will they not be able to sell goods from State Y to State X (even when they have registration in State X)?

There is no such restrictions whatsoever. Maintain proper records

multistate registration is not requied. , but it is pertinent from which state order is receied.