Am I still a step-dad?

TBagpuss

Step-children are the children of your spouse who are not your biological children.

So:
- They don't automatically inherit if you die intestate
- They wouldn't normally be still considered your step-children if you are divorced from their parent, although I don't think it would invalidate any existing gift in your will, as the rules only explicitly affect gifts or appointments of your spouse, when you divorce.
- an adopted child isn't a step-child, they are treated in every way* as if they were a biological child 
- If your spouse dies, I don't think that this would stop any of their children being seen as your step-children, as the marriage was till in existence when your spouse died, although you would be sensible to check with your solicitor if it was likely to be relevant. 
(*except in relation to becoming an heir to the throne or to some hereditary titles, which is unlikely to be relevant to most of us!)
OP, you say you don't feel it's fair that people with children's get a break with IHT. IHT in general isn't particularly fair. Married couples get bit advantages, despite the fact that being half of a couple us much cheaper, generally , than being single. People with children get benefits denied to those without - its not set up to be fair!