Firstly, input type checkbox will show you true or false automatically and you need not have separate template if:true.
For checkbox, you should use checked attribute for binding boolean and not value.
You can bind a formula to checked property.
Also, LWC components are 1-way binding. So, even if it shows the checked or not based on initial formula, further ...
Regarding your errors,
For error 1:
You are calling the constructor without any parameter, but you defined your constructor to accept two parameters.
For error 2:
co.asset__c is a lookup field (of Id data type), but you are comparing it against an SObject.
public static void ChangeOrderDuplicateChecker(List<Change_Order__c> cos)