There are a number of issues here.
Firstly, there's nothing to stop you doing training, so long as the training you do isn't incompatible with your being regarded as unfit for work. Skill have guides to the compatibility of incapacity benefit and study. However, their site appears to be down right now, so I can't link you to the page.
It is possible to do work whilst on benefits, depending on whether you get paid, and if so, how much. Again, like studying, the work that you do could call into question whether you are fit for work depending on the nature of the work.
There is a guide to working and claiming on here.
www.benefitsandwork.co.uk/help-for-claimants/work Do also take a look at the information on there about when voluntary work doesn't count as voluntary work.