There are lots of rules regarding income for ESA, so to give a brief outline, Earnings are accounted for, less a £20 disregard - holiday pay normally counts as earnings (if the person has left the job, this can be different).
The exception to the general rule that earnings are accounted for, is 'Permitted Work'. In this case, where the DWP has authorised the work, you can earn either up to £20 or £115.50 depending on what kind of permitted work has been authorised.
As regards charity donations - I'm not 100% sure what you mean by this - however if it is someone paying towards the mortgage of an ESA claimant, this would probably count as income for the claimant. If the person paying towards the mortgage also had an interest in the mortgage this may be different, but I won't speculate on that.
Let us know if you have a specific scenario and we can go into more detail for you.