Your two examples are correct for both being told and asking.
The two sentences that you are questioning are also correct.
For this AmE speaker there is a subtle difference between will you and would you, and shall I and should I.
Will you please
implies an immediacy, do it now
Would you please
is asking you to do something
if you are able to
if it's not too inconvenient
if you have the time
if it's not too much trouble
it is more polite.
Shall I is posing a question by offering to do something and looking for mutual agreement for that action.
Shall I make tea?
Shall I fetch you at 4?
Should I is asking for guidance of an action based on a rule or opinion: should or should not do.
Should I go to the dentist when I have a toothache?
Should I discipline my dog if he misbehaves?
Should I take out the garbage on Mondays?
From my experience, should is more AmE and shall is more BrE.
Could you do something
Is asking if you are able to perform an action and is related to can you but is more conditional in the way that asking for permission is
Could you get me a glass of water please?
Could you stand on your head?
Could you expand on this?
an answer might be
I could do that (for you) if I wanted to, but I won't
meaning: I am able to do what your request, but I don't feel like it