Is adding a css class to a <b> tag valid html/css

Yes, b tag can have all global attributes, including class. The full list of attributes, you can add to b element:

• accesskey
• class
• contenteditable
• contextmenu
• dir
• draggable
• dropzone
• hidden
• id
• inert
• itemid
• itemprop
• itemref
• itemscope
• itemtype
• lang
• spellcheck
• style
• tabindex
• title
• translate

You can also use any custom data attributes.

Finally, you can add also ARIA role attribute.

Of course. There's nothing wrong with that.

However, it's generally a bad idea to use class purely for identifying an element. Consider using something like data-reference or something, as this will be more correct (and more efficient on the browser not having to keep track of a class that's not used as a class)

Yes, this is perfectly valid. Absolutely nothing wrong with it.