One entry, and it is a room you have to ask to enter. That is the whole character of the city, really.
Not a Monday. And not without the letter.
Write ahead. I cannot say it more plainly than the entry does. The request is the visit: name what you want to see, say why, and give them a fortnight. Turning up hopeful gets you a very polite German sentence and a closed door.
Ask for less than you want. Six sheets looked at properly will beat thirty flicked through, and the staff will offer you the seventh themselves once they see you are actually reading.
Keep the afternoon empty. I have never once left a study room on schedule, and the plaza outside is a perfectly good place to sit and rewrite the list you came in with.