Can students bargain over admission date?
delay my possible admission for a year


In theory, yes, you can delay the admission for up to a year but you need to know the rules. 

As mentioned in the comments, this is called deferring. Each university/institute has certain rules regarding the deferment. At some places, you may not be able to defer the offer so long. While others, which allow the deferments for up to a term or two, it might be easier to delay for one semester/term (4 to 6 months) by providing a reasonable excuse. However, this can be extended for one more term (3 to 6 months) but in special cases and may require the agreement of the prospective supervisor, HoD etc. 


  Which points do I have to consider prior to send an e-mail to uni X when dealing with such an issue?


Try to know their rules through the website or by email. 

See what is the maximum period (P) they can allow you? 4+3=7 or 6+6=12 or ...

Does (P) satisfy you? 

If yes, then what would be the special conditions for the extension?

Would you be able to manage to deal with those special conditions?