PCTs commission care from hospitals and other healthcare providers for the population under their care (usually something in the region of 300,000 plus). They negotiate with the healthcare providers, argue about what has and hasn't been delivered, monitor standards of care (lots and lots of performance numbers). When I was working (a couple of years ago now) they also provided directly all the community health services, like district nursing, childrens therapies etc, but there has been a move to have those as stand alone services, and make PCTs just commission.
For the hospital services there's not much room to maneuver, because the hospitals hold the balance of power, and always have done (perhaps less with some smaller hospitals, but for my inner London PCT the power was very much in the favour of the very large teaching hospitals hands), but for smaller services, there is a lot of figuring out the needs of the population, consultation, finding the best service provider (which might be NHS, private or voluntary sector), negotiating contracts, and then contract monitoring. I seem to recall that we had something in the region of thirty or so contracts, and then some one off arrangements for patients who needed something different. PCTs are also where public health and health promotion sit. Our PCT also worked very closely with social care, so we had lots of joint schemes with the council, and the last reorganisation was to make sure that PCTs and councils shared boundaries to make that easier.
In answer to your second question, GPs already spend a fair bit of time on non clinical work, as the majority run their practices, and of course there is lots of paperwork associated with their work (referrals etc) too. Many will be on various committees and working on initiatives, also there are already GP consortia who are supposed to be involved in commissioning. In our area they were extremely reluctant to do this, as most had been opposed to fundholding, and a lot of resources had been dedicated to try and get them involved (as it was a performance criteria for PCTs to make progress). I'm not sure how you could require GPs to pick up commissioning, as they are independent contractors, so you can't make them do things very easily. Essentially you either have to pay them extra, or try and change the contract, difficult to do as the BMA are probably the most effective union in the UK.