Actually it depends on which kind of letter u r writing i.e formal/informal.if u r writing a informal letter that is to a friend then u can use idioms and phrase but if u r writing a formal one that is like:principal/bussiness person than idioms and phrases are not appropriate.
Yes it is possible.
if in formal letter , u could write it as
we want the agreement in black n white
if in informal u want to xpress about some incideny u could wrtite like
i ran a hens leg when the gardener saw me plucking the flowers.