These are questions best addressed by the corporate advisory service handling the sale of the business.

It is not necessarily a lengthy process to secure a PE deal. Some PE firms are well placed to take a quick decision provided, and this is an important caveat, provided you are well prepared and have all your ducks in a row.

And you have the advantage of a full management team and one (presumably) already motivated by a share incentive scheme.

It's imperative you have a good corporate finance adviser on board. It may well be that your best option is for the management team to raise finance independently and without relying on PE.

I must confess that the latter part of your post has lost me completely and I've no idea what you're trying to get clarified!