Parish councils have the power to run all of the services you mention, so there is no need to establish a new body to take them on. Creating too many committees may not be sustainable. External funding is available to assist the parish council with new services. It is normal for village halls and community centres to be run by a dedicated charity, but this is usually wholly independent of the parish council.
Using my parishes as an example, the village hall/community centre buildings belong to the councils but are leased on a full repairing and maintaining basis to the charities. If work is required to the fabric of the building, the council may make a one-off contribution if the work is either unaffordable for the charity or would jeopardise the charity's financial stability, however there is no ongoing funding relationship. Two of these community centres stand in council-owned recreation grounds that are included in the lease to the hall charity, so that the indoor and outdoor spaces can be managed together. The other two parishes manage their recreation grounds as part of the work of the council.
We have some historic welfare/education/general purpose charities, to which the council appoints some trustees, but always a minority of the total number, so the council can exercise no control over the charity. There is no funding relationship with the charities. The council also appoints members to the assessment panels of the local wind farm and power station community benefit funds, but again, a minority of the total membership. We're involved, for the benefit of our communities, but we don't seek to control.
With my many hats on, I talk to a lot of parish councillors and the vast majority operate along broadly similar lines to my own. Beyond that, I can't comment.