Caching the response from Sling Model, Sling Servlet

Yes sling model responses can be cached kn dispatcher if you you implement sling model exporter in your sling model class. Actually, you can only cache the response on dispatcher which have file extension at the end of the response url. Check below to see how you can implement sling model exporter in aem https://experienceleague.adobe.com/en/docs/experience-manager-learn/foundation/development/develop-sling-model-exporter

normally, it’s not recommended to cache the 3rd party api response as it might change any time. In your use case even the 3rd party api response is same for a week, you don’t know at what time it will change in the future and you might have problem in identifying the exact time of the 3rd party response change and would have difficult time in doing those cache response flushed from the cache. So, it totally depends on you to decide how you can handle the flush of cached response in case it’s changed 

1: Caching sling model response:

From my sling model, I am hitting the 3rd party API. (API response will be same for, say 1 week). So, is it possible to cache the sling model response?

as mentioned in the article caching from sling model is not the right way.

Sling Models are designed to use or mean to be Stateless - and scope should be limit to request (Request scoped) - caching within a Sling Model can lead to unexpected behavior.

2: Caching sling servlet response: I heard, response from sling servlet is cacheable. If yes, I need to mention anything in sling servlet class, Dispatcher?

Yes, This can be achieved. 

In AEM we can cache the response from a Sling Servlet. This is typically done at the dispatcher level. You don't need to do anything special in the Sling Servlet itself, but you do need to configure your dispatcher to cache the response. This involves setting up a dispatcher caching rule that matches the URL pattern of your Sling Servlet.

ex: Sling Servlet is accessible at a URL like - /content/myapp/myservlet

/cache
{
/rules
{
/0000
{
/glob "* /content/myapp/myservlet*"
/type "allow"
}

3: Caching the response from 3rd party API: What is the best way to cache the response from the 3rd party. I know that 3rd party API response is constant for 1 week. Even, if the API response changes for every day, I dont mind. Still will use the cached response for a week. 

one common approach is to use a caching HTTP client. This can be configured to cache responses based on their HTTP headers, or you can implement custom caching rules.

CacheConfig cacheConfig = CacheConfig.custom()
.setMaxCacheEntries(1000)
.setMaxObjectSize(8192)
.build();
RequestConfig requestConfig = RequestConfig.custom()
.setConnectTimeout(30000)
.setSocketTimeout(30000)
.build();
CloseableHttpClient cachingClient = CachingHttpClients.custom()
.setCacheConfig(cacheConfig)
.setDefaultRequestConfig(requestConfig)
.build();

use this - CloseableHttpClient to make API calls or requests and apply the responses will be cached as per the configuration.