IF: Can a fellow who organises a conference (not only attending one) claim the related costs on his/her project, and if yes, in which category?

Yes, the fellow can claim costs for such a conference from Contribution to the training expenses… if the conference is related to the project.
S/he might expect some results from the conference that could be important for the project, s/he can also present the project (and the MSCA) during the conference (dissemination activity). And eventually organising the conference might be a beneficial experience for him(her.

Travel & accommodation expenses of invited speakers can be claimed within the project but as those costs might become high we recommend to pay special attention to the budget – if there will be still enough funds in Contribution to the training expenses… category to carry out all other project activities. 

(information by NCPs)