Let me offer a different perspective to you, before answering the questions, as your post almost screams the following:
" I don't like him, I don't like what he does, or how he does it"
" What he ever he does do, how dare he charge £250?!"
Setting aside room for improvement,if he were replaced, would you take on what he does, voluntarily, and for no, or a small amount of, money?
Powers To Do As long as the service or work is permitted under the lease and the cost and solution is fair and reasonable, they are not required to consult, expect for qualifying works where any flat pays £250+. Directors are of course accountable to shareholders
Directors and AGM You will have to look at the Articles of Association to see how and when directors are appointed. If not on your file Companies House sell them on line.
Items in the Hall Bluntly refuse should never be left in the hallways it's extremely rude to neighbours to expect them to come home to see your rubbish lying in the hall 'Your bin or the common bin'. Your tenant was wrong to assume they could put their bike in the hall - it's not a right in their tenancy. The lease need not say no to items, your rights to the area are set out in your lease and would have to be expressly granted, and in most cases are restricted to allowing you to pass through the common area.
If it is safe to leave items in the hallway and it is not to the detriment to the block as a whole you might unanimously, not as a majority, might agree to place for a buggy and a bicycle or plant. This is because each owner is entitled to the benefit under the lease not to have items in these areas. No bike , no buggy...
A meeting focusing on the problems is an idea, not recrimination, but be prepared to accept that before you have him sacked and arrested as your post implies, if he isn't going to do the paperwork books annual filing arranging for jobs to be done and paying the bills, are you?
Based on the information posted, I offer my thoughts.Any action you then take is your liability. While commending individual effort, there is no substitute for a thorough review of documents and facts by paid for professional advisers