Is it rude to chase someone who has not replied?
No. A single reminder that carries the deadline's reason reads as organisation, not pressure, because it asks about the event rather than about your worth. The rude version is the third chase; one well-timed nudge is just hospitality with a diary.
How much should I charge myself with waiting?
Do not wait and wonder; set the reply deadline a week or so before you must hand numbers over, and treat the date as the decision. Guests who care answer early regardless; the deadline exists for the forgetful, who are usually the keen ones.
Should I let people answer maybe?
Let them say it in the chat; a tracked maybe helps you less than a tracked no, because you cannot seat a maybe. Keep the page question to yes or no, with plus-ones inside your limit, and hold the soft landing for the conversation.
What is a good deadline to set?
Work backwards from the number's consumer. The caterer needs final counts days ahead, a venue booking a little before that, and your head needs a margin to chase politely. A week or two before the event is kind to everyone; a wedding with travelling guests wants longer.
Does any of this work for a group invitation?
It works better there, because a page link survives a noisy group chat in a way a text invitation never does. One question, one button, one list, and the jokes can carry on underneath without costing you a headcount.