Quote Originally Posted by justinwyllie View Post
If the man is called Mr Иванов is his wife to be called Mrs Иванова? i.e. the surname has to reflect gender?
Yes, most Russian surnames have gender variants. Not all of them though.

Quote Originally Posted by justinwyllie View Post
Does this also apply to unmarried women
Yes. Unlike Lithuanian, in Russian, there is no distinction between married and unmarried women’s surnames.

Quote Originally Posted by justinwyllie View Post
e.g if the girl's father is Илья Петрович Иванов she should actually be called e.g Эльвира Ильева Иванова? (assuming her first name is Эльвира)
The surname is OK, but the patronymic from the name Илья should be Ильинична (pronounced like /ильйи́нишна/). An irregular one. Masculine form is Ильич /ильйи́ч/.

Quote Originally Posted by justinwyllie View Post
Also - how do female first names decline? e.g Марина - will this be like the feminine noun ending in -а or like an adjective?
First names decline like nouns.
Your example is a bit amusing though since there is also a female surname Марина which declines differently (and also has a different stress)

first name last name
nom, Мари́на Ма́рина
gen. Мари́ны Ма́риной
dat. Мари́не Ма́риной
acc. Мари́ну Ма́рину
instr. Мари́ной Ма́риной
prep. Мари́не Ма́риной