1. Just my middle tabs are not displaying fully horizontal. (other tab positions seem to be fine) See attachment 1.

I don't see any issue in your screenshot. What are you expecting them to display like? The tabs just flow inline 1 after another and will overflow to a new line if needed. They will not be perfectly and equally sized.

2. I use this (activity module + CB) on two sites with the same template and majority of settings, template settings I believe are the same. Yet the activity module displays at different sizes for each. Attachment 2 & 3...

There is no limit to the stream size. It's entirely based off its container. If you're using the module then you need to use a module position that gives it enough room or it's going to look squashed. Same for component content container. This should all be configurable from your template. The module sizing is also affected by the bootstrap parameters in the modules parameters, but that's all handled by Joomla so whether it does anything or not is up to the template.

3. Putting a link in the activity stream or by inserting a web address into the sharing a link option has the desired effect but the link goes to www.mywebsite/thelinkedwebsite, bringing about internal server error 500.

You need to provide a live site URL. Meaning it needs to include the full domain. Aside from that maybe you've a SEF extension or URL rewrite rule in htaccess that could be altering the URLs as there is no code in CB Activity to prefix shared URLs with Joomlas live_site and am unable to confirm in multiple tests.

Ok, with links on stream, when I put in the http:// it works correctly. Does it not pick up its absence and adjust?So if www.whateversite.com type in their domain as they would know it well without having to copy and paste - they get system 500 errors on their links. Is there a setting to rectify that at all? Auto action or something I wonder.

Ah, ok I understand your issue. Was able to confirm and have created a bug ticket to fix for next bug fix release.

forge.joomlapolis.com/issues/5396

The tabs should align horizontally and overflow yes - but in this case they shouldn't overflow. See new attachment where they stack up unnecessarily in middle position but fine on the position below.

Looks like you're using Canvas Main Left, which is designed to be at that size. Use a different position and it should display fine.