Ye gods, where do I start. Well, I'll give it a shot:-
Please could you explain how the Type Rating exception works viz a viz permit aircraft, aerial work and public transport.
For a start type ratings are a completely separate issue. You either need a type rating (such as for an R44 or a Hawker Hunter) or you don't (let's say for a Europa).
To gain a type rating, or a licence (say moving from NPPL(M) to PPL(SEP) this can be done by an FI on a PtF or Private CofA aircraft solely owned, or on any Public CofA aeroplane. There are exceptions to this, for which CAA has granted exemptions - for example type-approved microlights, or certain warbirds used for conversion training (JPs etc.).
Can a PPL train and check out another PPL in a Permit aircraft and charge for the use of the aircraft?
I'll use the terms trainee and trainer here or I'll disapear up my backside in terminology. If the trainee is technically rated for the aircraft but no hours on type, then they can be checked out on that type by another PPL who is. But, they cannot pay/charge for this, nor can anything be paid for use of the aircraft except the actual running costs.
Can a CPL who does that charge for his services?
Only if they hold an FI rating valid for the aircraft type.
I've seen adverts for Harvard rides at Shoreham in the aviation mags for years
The majority are on Permits, but a few are on Public CofA - presumably including those being advertised.
I don't see personally a problem with a nominal stake, because English contract law only requires that something of tangible value, satisfying both parties, changes hands in both directions for a legal contract. There is nothing to stop me selling you my house or one of my aeroplanes for £1 so long as I am satisfied that this was fair exchange. Nobody but the parties to that contract are, so far as I understand, considered qualified to judge what constitutes fair value.
Where's Flying Lawyer when you need him?
G