1) How to check unused object count & total object count
I am not aware of any command that will give you a summary of what objects are not in use and the total number of objects. To see which objects are not in use you would need to issue a show run | include OBJECT (where OBJECT is the name of the object you want to see configurations for) and see if any NAT or ACL statements use the object. If the object is not referenced anywhere then it is not in use.
for the total object count you can issue the show run object command. this will list all configured objects, you will need to count them to get a total object count. It is teadious but unfortunately the only way.
2) How to check total policy count/total nat rules/total xlate connection
For the total nat rules count you can issue the command show nat
for the total xlate connections you can issue the command show xlate count. This will give you a total in use count of the xlate table and the most used.
I am unaware of a command that would give you the total policy count. Here I believe you would need to issue a show run policy to see how many policies are configured.
3) Is there any config size limiation for ASA
The configuration file is stored in Flash so the only limit to the config file size is the amount of Flash memory you have installed in your ASA.
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