Thank you for the answer! None of this is true as far as I'm aware. I'm also sure my employer would actually be pretty supportive.
You need to be sure :)
The above list of requirements is in essence what most of the UK and EU check for when doing checks of patent and IP law.
I am not a lawyer though, I'm in engineering... so of course, get your own confidence that this approach is good for you.
Most employers would be cool with extra-curricular things (many demand it on CVs!), but you never actually know until it happens.