Change of name on certificate of stocks

Short answer, it's probably fine under the terms of your coop proprietary lease for the coop to bill the unit's shareholders for attorney costs incurred that are specific to the unit. You can double check the lease if you want; that would be the authoritative document.

Not sure why it would take four hours for basic research and answering questions; did you get a response regarding documents to be filled out or retrieved?

You might do better for basic questions if the managing agent can answer, especially if they have someone at that office who specializes in setting up transfers. Or ask if they anticipate billing additional hours on this and if so ask for an estimate of how many more.