No it isn't. They key is that management and board are against it and the deal is still pursued by the (potential) acquirer. It is perfectly possible to initiate a conversation regarding an acquisition and this is not a hostile takeover per-se though it could develop into one.
Musk made an unsolicited, and what seems to be a non-investment choice, purchase of almost 10% of the shares and wanted to join the board. As far as I can tell, the board made his board seat contingent on Musk not buying more than 14.9% and Musk said no, and a few days later offered to buy the company outright. Now Twitter is taking moves to prevent a hostile takeover. That sounds like a hostile takeover to me.
Yes it does, and this is underlined by the fact that they adopted the poison pill proposal. Though, in the past such tactics have been used just to get a better price, in investment banking 'no' doesn't really always mean 'no', it may just mean 'really, no, not at this price'. That said this is already a pretty premium and they might end up regretting that move if they really are after the money and don't have a different motivation.
What? This is not just wrong, it's comical to even think of what it would mean if it were true. The board would have to clairvoyantly foresee any possible acquirer who might be interested in the company, or else reach out to every company and individual in the world, stating its willingness - or otherwise - to be acquired. That would be, uh, quite something.