Its not available OOTB, as suggested by @gaurav, you have to customize JSP

I am not clear on what the question is. If its about link, you can have simple links to social media pages and icons can come from image or css.Would appreciate if you can be more clear. Thanks

Can also make that component part of base template, which will be automatically inherited.

You have to customized that part, start by looking at the core component search /apps/core/wcm/components/search/v1/search

It's not available OOTB and RTE is tightly coupled to work with HTMLAFAIK, only place where markdown can be used is Content Fragment. You can have a look and see if it works for your use case.

Target integration will always happen via two approaches for AEM on-premise or Adobe Managed Services1. AEM > Config Launch and the in Launch configure target (cloud config)2. Directly configure target in AEM (cloud config)Target should be able to access it your aem if you are trying to use element ...

Yes, you can implement it.Please complete details here Adobe Experience Manager Help | Creating a Custom Authentication Handler for Adobe Experience Manager 6.4

Both sitemap.xml and robots.txt contributes towards SEO of the site but by searching different purpose. I am linking few external threads you can read for detailRobots.txt vs Sitemap -- Who wins in a Conflict - Webmasters Stack Exchange What is the difference between robots.txt and an XML sitemap? -...

Yes, you can use 3rd party library.Change the OOTB workflow and add your custom workflow process which use library like ffmpeg to inject watermark in video. This can be a CPU intensive operation depends on video length and quality.Make sure to read the license of the library you choose you use.GitHu...

Answers to your question.1, yes, both are independent and each has their own purpose.2. AEM author should take care of this which creating content3. Same as 2nd, Author should be trained on SEO and taken care while creating content.