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. In general, you can easily 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 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?

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?