I have talked to my recruitment officer multiple times about issuing me a statement for health and care visa

I have a few queries.

  1. I have talked to my recruitment officer multiple times about issuing me a statement for health and care visa. She is adamant that they issue COS only for tier 2 category. I explained to her that it is a tier 2 subcategory and there’s no need to modify COS either. She’s quite inflexible about it. What do i do? Can i email the person whose email is listed on the COS for help? I don’t want my HR to think i’m being fussy.
  1. How long after joining a job can i leave it to join another job? Are there any legal ramifications if i leave a 1 year contract in the middle to take up another post?
  2. The relocation policy states that it includes reimbursement of expenses for “Journey to take up post- Receipted expenditure for relocating employee anddependants, including overnight stay andassociated expenses (if required). Limited to one occasion only and one vehicle. Travel Expenses at PTR, or NHS Grampian Lease Car Rate (where applicable) or, alternatively, economy travel by rail or air.” Does visa cost come under the umbrella of “journey to take up the post”?