Scrum questions

User stories are only one method that can be used to create PBIs.  They should have enough information to invoke a discussion. 

Remember that Scrum does not dictate what the Scrum Team uses here, so your mandatory question is moot.  You have already asked the right question though, which the Scrum Team should be able to answer:  "What if acceptance criteria is not mentioned?"  Once of the obvious answers will be that how can the Developers determine that they have completed work on a PBI that meets the needs of the stakeholder that requested it? 

The SG does not mention sprint backlog refinement, so I am presuming you meant product backlog refinement.  Product backlog refinement is not an event in scrum; however, it is an event in Nexus.  BTW, grooming was replaced by refinement some years ago.

If product backlog refinement is not done, the PO will not be able to order the PB correctly as none of the PBIs will be decomposed enough to be ready for selection based on the agreed upon sprint goal during sprint planning.   

1. Is there any specific pattern/steps to be followed while writing user stories?

A user story is a placeholder for a conversation about a potential requirement. There are 3 notional parts to it: card, conversation, and confirmation. What does that tell you about the extent to which a user story is "written" at all?

2.  Is acceptance criteria mandatory with user stories ? What if it is not mentioned ?

How would their satisfaction then be confirmed?

3. Is it mandatory to conduct Sprint backlog refinement /grooming session? What are the consequence if this scrum ceremony is skipped ?

There are no ceremonies in Scrum, though there are events, and Sprint Backlog refinement is not one of them. There is however Product Backlog refinement which is an activity.

Would the work be "ready" for selection in Sprint Planning, if Product Backlog refinement were to be skipped? Does the Scrum Guide describe it as being optional?

For your first two questions the answers should come from your team. Those are procedural questions and the Scrum framework does not describe process. Also since User Stories are not mentioned once in the Scrum Guide, these questions are not Scrum related.  If you want to know more about User Stories, you should research the eXtreme Programming space since that is where they originated. 

Is it mandatory to conduct Sprint backlog refinement /grooming session?

i'm going to get a bit picky about your language as other have.  Sprint backlog refinement is not mentioned in the Scrum Guide.  Refinement of Product Backlog items is but it is not one of the mentioned events.  (There are no ceremonies in Scrum).  The word "refinement" is used once in the current Scrum Guide in the section that describes the Product Backlog (I added some emphasis)

Product Backlog items that can be Done by the Scrum Team within one Sprint are deemed ready for selection in a Sprint Planning event. They usually acquire this degree of transparency after refining activities. Product Backlog refinement is the act of breaking down and further defining Product Backlog items into smaller more precise items. This is an ongoing activity to add details, such as a description, order, and size. Attributes often vary with the domain of work.

Notice that there is no mention of a ceremony, event, or even meeting.  It is consider an activity that goes on continuously.  Also notice the paragraph indicates that only items that have undergone enough refinement for the team to feel it can be "Done" within a Sprint are pulled in.  That leads me to believe that there is no Sprint Backlog refinement. However the Scrum Guide does say this in the section describing the Sprint Backlog

The Sprint Backlog is a plan by and for the Developers. It is a highly visible, real-time picture of the work that the Developers plan to accomplish during the Sprint in order to achieve the Sprint Goal. Consequently, the Sprint Backlog is updated throughout the Sprint as more is learned. It should have enough detail that they can inspect their progress in the Daily Scrum.

So there can be updates made to the Sprint Backlog as new information is learned.  Technically that could be considered refinement but again no mention of any event, ceremony or meeting.

What are the consequence if this scrum ceremony is skipped ?

Since there is no ceremony there are no consequences to skipping it.  However, if the team is not spending time refining Product Backlog Items, there is no way for them to know if any of them are capable of being "Done" within a single Sprint.  Also by not refining the Product Backlog Items, the Product Owner will not be able to do meet their primary duty of maximizing the value of the product resulting from the work of the Scrum Team and will not be able to appropriately order the Product Backlog.