If you are being asked to upload a covering letter as an attachment, then you lay it out as a standard, formal letter, with addresses, salutation and signature block. In this case you do not need to put the recipients address above the salutation.
If you are asked to upload a covering letter into a plain box on a form, then skip the addresses, salutation and signature block, just put in the main body of the letter.
As with any formal letter, if you have addressed it to a person by name, then you sign in off Yours sincerely. If you address it to any generic title, Dear HR Manager or Dear Sir/Madam then you close with Yours faithfully. In neither case is the second word capitalised.