[SalesForce] Hyperlink formula field to open in the same page

I don't think that it is possible (or even logical) to achieve what you are asking. How can you have your Object1__c pointing to an Account record that has not been created yet? If you are inserting an Account record, the related list in your question will always be empty, since no Ojbect1__c record will be pointing to an Account record that doesn't even exists yet.

Aside to this, if you need to check if your Account record has any records in a related list, you have two options depending on the type of relationship between Account and Object1__c.

1) If you have a Master-Detail relationship between the Account and Object1__c, you need to create a Roll-up Summary field on your Account object that will COUNT the number of related Object1__c records. Then, in your validation rule you need to check the value of this Roll-up Summary field to see if it is 0.

2) If you have a lookup relationship between the Account and Object1__c, you can't use the Roll-up Summary field, but you can use a trigger that will perform the similar logic. You can run this trigger on before update to count the number of related Object1__c records and throw a validation error using the addError(..) method on sObject class.

Also, as I mentioned at the beginning of my answer, note that this validation only makes sense on Account record update.

I solved it like this:

Create a formula field on the object that you are linking to:

HYPERLINK("/"&Id, CaseNumber ,"_parent" )

And get that field of the record you are trying to link on a display text element in flow