what conference costs (e.g. travel and accommodation for key notes speakers, refreshments during breaks) can be claimed as a research costs?

Yes, the fellow can claim costs for such a conference from Contribution to the training expenses… if the conference is related to the project.
He might expect some results from the conference that could be important for the project, he can also present the project (and MSCA) during the conference (dissemination activity). And eventually organising the conference might be a beneficial experience for him.
Travel & accommodation expenses of invited speakers can be claimed within the project but as those costs might become high I would 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.