Insurance (is it compulsory?),
YES. Good grief, of course its compulsory - what would happen if you were not insured and there was a fire, as a result of something YOU'd done? All your liveries would sue the pants off you and you'd go bankrupt. Or what if one of your liveries is riding in your field, and is badly hurt or even killed? You
have to be insured to run a livery yard, yes. That would really be your biggest out-going.
Facilities - well, how long is a piece of string? Fields, stables at a minimum but then there are schools, walkers, secure tack rooms, etc. Assuming you don't already own a suitable farm or piece of land, you'd have to find a suitable yard to rent, which is likely to be extremely expensive, and would really eat into your profits. i have to say that i personally would not move to a yard, however nice it looked, that did not have a decent-sized all-weather school, that was lit so it could be used after dark. Again, having a proper school is another expense and it will affect the amount of council business rates that you pay.
A member of staff or two is helpful if you want to offer any more than pure DIY livery. If you employ someone you have to pay tax and NI on their wages, plus you will need further Employers' Liability Insurance.
Since it is a LIVERY yard, you don't really have to do anything about acquiring horses, i think you'd find they'd come to you ! When you look at all the costs and downsides, you start to realise why most YOs are barking mad - you have to be, to want to do the job !