Hi Alex,

Google normally should not have had interruptions for indexing new links while it was not updated. This could even depend on how much time is elapsed.

If you updated from a quite recent version of JSitemap, for example 3.x or 4.x series, you should not require particular operations. If you updated from an old version such as 2.x series, you could delete and re-create data sources for third party extension such as K2 to ensure to avoid issues.

Don't rely to the order of the links listed in the Links Analyzer, obviously that's only a casual ordering used in the component based on the data sources. Search engines work only with links priority values, the ordering of links doesn't matter at all. I don't see particular issues in your analyzer list, everything is good about contents and pages health.

My recommendation about using the full potential of JSitemap, is use it to improve titles and metadescriptions. Also use the SEO spider to identify potential SEO improvements and enable the auto ping feature.
The Search Engines Metainfo supports all extensions integrated through data sources and in the sitemap, obviusly including K2.

Best,
John