There are a number of issues here, but to take your questions in turn.
1) No, any life insurance policy should be written with a trust ‘wrapped around’ it. This will mean that the payout from the life insurance goes directly from the insurer to the trust, and as a result never falls into your taxable estate. This will potentially save 40% inheritance tax on the payout. Most life insurers have an off the shelf flexible trust deed that will deal with this. If you need a bespoke trust deed drawn up, expect to pay about £450 plus VAT, but based on what you have said the standard type would probably do the job. Any IFA worth his salt would be able to set the life assurance with flexible trust up for you. For a bespoke trust you would need a specialist lawyer (declares an interest and waves).
2) The money would be managed by the trustees, they are bound by the Trustee act 2000 which lays down what they can and can’t do. The answer depends on when the money is paid out and how much. At the moment a good option might be to buy a house and rent it out using the rental income to pay for the maintenance, education and benefit of the child. That’s just one option again a suitably qualified IFA would need to be consulted by the trustees at the time (it is one of the requirements of the Trustee Act). You can lay out what you would like to happen in an expression of wishes document, so things like monthly payments to the ex can be dealt with. An expression of wishes document is guidance to the trustees, so not legally binding, but it is normal to have one and in my experience most trustees will work in line with the wishes.
3) The other option is to let the money from the insurance fall into you estate (by not having a trust attached to it) and then dispose of it according to your Will.
In any case you should have a current and valid Will that deals with your affairs and you should consider making a Lasting Power of Attorney as well.
If you want to know more my e-mail is in my profile.
Regards
Nick.