Selling services to the UK - is it doable / feasible?

Hi folks, looking for some advice (as per usual )

I do some volunteer work with a UK company, mentoring school students / lecturing on my area of expertise, that sort of thing. All virtual obviously. The lectures are attended by a wide audience - not just the students themselves, but each of their own mentors too, many of whom work for big corporations. Recently I was approached by someone who had seen one of my lectures, and asked if I would consider consulting for their organisation, running a lecture series over several months on a paid basis.

I haven't responded yet, but I quite like the idea, so I'm in research mode to understand the practicalities.

1. Taking on side-work alongside a full-time job: permit-wise, I believe I'm allowed to do this, as an EU B-Permit holder. Job wise, my contract states that I require permission from HR, and that the side-work must not present a conflict of interest. I'll raise it with HR if I decide to proceed.

2. Understanding the requirements for operating as a sole proprietor: I think I get the gist of it. The trading name must include my surname, I would need to register in the trade register, I'm responsible for submitting a tax return on earnings... I think sole proprietors also have to make contributions into AHV & one of the other pillars too? I'm sure there's other stuff I haven't thought of...

3. How to invoice someone in the UK for work carried out in Switzerland: haven't got the faintest idea how any of this works

Hit me with your advice / constructive criticism / wisdom. If it turns out to be way too complicated, I'll bin the whole idea and just continue with the pro-bono stuff. But I felt it was worth investigating first.

Cheers all!

Bueller... Bueller...

Anyone had experience with this sort of thing before - selling a virtual service to another country (and billing for it)? I'm grateful for any advice (or pointing me in the direction of someone / a service that might be able to help too)

1. Correct

3. Raise invoice. Send to customer. Get paid. Might be issues regarding MWST.