Deadline for migration to UC

Hello, I have a question. I received my notice for migration to Universal Credit (UC) on 21 February 2025. I must claim UC by 22 May 2025 to keep receiving financial support (I’m currently getting ESA and Housing Benefit, apart from DLA). I’m due ESA on 7 May and on 21 May. I have not yet started my claim for UC - I’m wanting to leave making my claim until 21 May, and completing the online form on that day so that I can get the final ESA payment on 21 May. (Shall be very short of money during the five week wait while my UC claim is processed.). Can I leave claiming ‘till 21 st, if I complete and submit, the application that day or could doing so make it go over the deadline of 22 May? Another question is regarding my Housing Benefit (HB). My rent increased on 7 April 2025, so I informed the city council by letter sent on 21 March. I didn’t hear from the council, so I completed an online change of circumstances form on 22 April. I’m worried that I won’t hear from the council by, with confirmation they’ll increase my HB, before my UC application deadline. I’m concerned, therefore, I could lose money regarding the amount included in my UC for my rent. Also with council tax: I have been getting full council tax support - would I still receive this under UC? Do I have to reapply to the council for council tax support when I apply for UC? Many thanks.