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You'll definitely need to upgrade to NSM Better Meta 1.1.5a - the release notes mention EE 2.6 compatibility, which likely includes accounting for the database changes which it brought (specifically, the removal of the dst_enabled column).

Below final solution based on category custom fields (thanks to Mark), SEO Lite module, Low Seg2Cat and GWcode Categories plugin in case someone will have similar problem which I had. {if segment_2!="" && segment_3==""} {exp:gwcode_categories show="{segment_2_category_id}" custom_fields="yes" style="linear"} {embed="includes/.header-...

Try using the attr_safe modifier on your tag (where the value is generated, not the layout tag) - https://docs.expressionengine.com/latest/templates/variable-modifiers.html#attr_safe - that will convert special characters to HTML entities which should work.

Well, first of all, your {exp:channel:entries} tag has zero parameters, meaning you have little control over what's being loaded unless it is detecting it from the URL. I'm also guessing it's possible this Channel Entries loop lives inside of another one, which won't work. You'll have to provide significantly more information for us to give you a real answer....

I know this will sound silly but have you tried changing your quotation marks within the EE tag to single quotes. I run into this issue all the time even though it 'looks' like it shouldn't be an issue. <meta property="og:description" {exp:streeng allowed='none'}content="{pages_summary}"{/exp:streeng}> I always use single quotes ( ' ) within an EE ...

Why not just create additional Category Custom Fields? They are quite limiting but a Text Input for Keywords and a Text Area field should suffice for meta data. You can read more about them here: https://ellislab.com/expressionengine/user-guide/cp/admin/channels/category_field_management.html

there is an easier way to do this with SEO Lite, check out this gist which has an example: https://gist.github.com/bjornbjorn/4039233