I want to use first deployment in this link (active/active all-in-one). But the question is here that can I add one all-in-one APIM in DMZ zone or not? I want to use this deployment pattern that cited in the link for my internal APIs and the APIM (all-in-one API) I want to add in DMZ zone for external consumer and APIs. Especially without any Gateway component, Because If I want to use Gateway component I can use deployment pattern 4 (Internal/External API Gateway Separation), but pattern number 4 is so complicated for my usage of APIM. So Can I have deployment pattern number 4 (Internal/External API Gateway Separation) with component design of pattern number 1 (active-active all-in-one)??(no separation and no Gateway)
Under deployment patterns I believe you refer these https://docs.wso2.com/display/AM250/Deployment+Patterns
can I add one all-in-one APIM in DMZ zone or not?
Nothing prevents you to do so.
Now the question is - do you want to have a completely separated APIM environment in DMZ? Do you plan to separate users, database, throttling, key management ... too? It's all fine. Then just have a separate environment in DMZ.
If you want to centrally manage APIs, users, keys, etc then you can configure the DMZ instance to use internal KM, TM, and analytics. And effectively you will get pattern 4. For KM and TM - you don't need to install separate instances (as described in the pattern). You can use the same "all-in-one" instance from the internal network.
Especially without any Gateway component,
The "all-in-one" APIM contains the Gateway component. Effectively the Gateway component is full APIM installation, just have disabled some management modules providing a profile parameter. From the installation point there's no different between installing full APIM or gateway.