if you give your company email id - AMS will enable the new relic access, this is the same process , we generally follow. You can ask your AMS, what is ECC id and the process to get it.

you can create account with your company email id in new relic: https://newrelic.com/signup?via=loginand send request to your AMS (Adobe Manager Services) support to enable the access.

If the issue only with Unit tests, can't you ignore for this class?, if not, the only option is to update the depricated classes

you can update to SP7, there are several issues addressed related to Move pages https://experienceleague.adobe.com/docs/experience-manager-65/release-notes/service-pack/sp-release-notes.html#install see the Sites section 

you can do overlay https://experienceleague.adobe.com/docs/experience-manager-65/developing/extending-aem/customizing-consoles-touch.html?lang=en#extending-aem overlay this path to /apps and select the option (check sling resource merger sling:hideProperties)/libs/wcm/core/content/sites/jcr:content/...

How you are updating your custom expiration date?, is it through service or workflow?. you can add logic by getting the resource there itself

It is better to rewrite http client code to newer version of apache.http(4.x).How about your regular class functionality?

For wknd tutorial, what are the issues you are facing?

what adapter are you passing on your Sling Model.adapters = {Carousel.class)

Instead of customizing the status, why don't you set or update prism:expirationDate value with your custom expiration date. That will automatically set the EXPIRED flag on Asset. custom:expirationDate = prism:expirationDate