addResults return empty array key

That seems like a problem in the Solr module.
However, I'm pretty sure it's either known or already fixed. When using dev versions, such incompatibilities currently occur very frequently. For that reason, you're advised to only use compatible Alpha releases (or be prepared for the consequences).

A new set of Alpha releases is however scheduled for today or tomorrow.

PS: It seems you (like many others – it's really easy to misinterpret) are confused by the "Issue tags" field. As the guidelines state, they aren't meant for free text tags related to the issue, but only for specific categorization purposes, usually by module maintainers.
So, if you aren't sure your current usage is correct, please just leave the field empty.

Does the error still occur if you use Search API 8.x-1.0-alpha16 and the latest dev of Search API Solr Search?

-        if ($field->getValues()) {
+        if ($key = $field->getCombinedPropertyPath() && $field->getValues()) {
           $values[$key] = $field->getValues();
         }

@divined:
Please post a patch. I can't see which file you're addressing.

@mkalkbrenner:

Just a small perfomance fix for the #1 patch.

Solr return two fields: search_api_language and search_api_datasource, which not have a definition data.

Solr return two fields: search_api_language and search_api_datasource, which not have a definition data.

I don't think that this is still the case for the latest dev version. Can you verify this?

Confirm: no problem in dev version.