BNCBG Trustees do not believe there is an automatic right of way across the whole Churchyard. In theory access is likely permissive; only for the purposes of tending or servicing graves or attending a funeral. Where Rights of Way exist they probably rest with the PCC who do not appear to be minded at present to restrict access.
If there is damage or loss to memorials anywhere within the Churchyard boundaries making good that loss or damage is the responsibility of whoever erected the memorial (usually who paid for it, or whoever inherited it as perhaps an unstated residue of settlement of an estate?). Insurance may be available via Domestic Household Insurance policies (Check the small print: Property outside the home?)
Undesirable activity cannot practically be managed or deterred by the Trustees. The vigilance, responsibility and community spirit of Churchyard users is relied on to report suspected or actual undesirable activity to the Police. Smart phones with cameras are soooo helpful in this respect
Please use the contact facility to report or comment on anything else.