Of course, all is subject to change but at this time you can't be in the water after 7pm., must wear a mask on the beach/boardwalk, no fireworks. But, you should be able to walk/hangout on the beach late night. I don't believe they are allowing any tents or the like though.

Насколько мы поняли местных - не разрешено.

There are few types of lockers in the area smaller ones will fit a small suitcase, the bigger ones can fit mid-size luggage, not one of those big ones normally people used to travel.

Да август самый пик сезона. Весь пляж в зонтиках и надувных кругах. Очень много людей. Все купаются.

1 августа, но есть те кто купается и в июне в холодной воде

Добрый день. Можно, только придется пройти немного пешком. Станция так и называется Haeundae

There are many luggage storages at the subway station (Haeundae st.), tourist information center and most of changing room on the beach as mentioned by the official from the Haeundae dictrict office.

I did not see any lockers. The hotels might store your luggage for a short period.

Busan has mild weather not as cold as Seoul. The temparture here is Busan has been over freezing point most of the winter days. Yes, Chrismas day is not a festival day in Korea and it is a normal holiday. Everything is OK wtih Bus, Subway, Taxi and Train. Yes, you can take subway all day in a year around

Hi, you mean Busan Port Terminal? I don't swim so I can't provide a definite answer. But I guess it is not advisable to swim near the cruise ships. From the map, you can take bus from Busan station to Haeundae Beach, it takes around an hour.