Just a quick follow up: If a player has a 4 conviction and 4 discipline along with a +1 power focus to fire spells, can he safely call up 5 shifts of fire spell despite not having the discipline of an equal value? Also, would he be able to create a fire rote this way?
I'll add a couple of minor things to what others have said. First, it might help clarify things to understand that what a "+1 power" bonus means is that the spellcaster increases his Conviction by +1 for purposes of casting a spell of the appropriate type. (Similarly, "+1 control" just means that the spellcaster increase his Discipline by +1 for purposes of casting spells of the appropriate type.) So in your example, the spellcaster could -- when casting fire spells only -- do anything a spellcaster with Conviction 5 and Discipline 4 could do. Tedronai's summary gives you the spellcaster's options here.
A couple of other things to note:
First, you mentioned "+1 power focus to fire spells". A focus needs to more specific regarding offensive vs defensive, so this focus would need to be "+1 offensive power to fire spells" or "+1 defensive power to fire spells".
Second, as Sinker noted, Fire is not the same as Seelie, even if casting fire-like Seelie magic. So if the character only had Seelie magic, then he'd want to define his focus as "+1 offensive (or defensive) power to Seelie spells". If the spellcaster has both Seelie magic
and Evocation, then he gains the option of mixing the two into spells. This allows you to use your Evocation bonuses along with the benefits granted by Seelie magic. So, for example, a Summer Fire spell could make use of a power bonus for Fire (from an Evocation specialization or focus) and also downgrade the Toughness of Winter enemies. In this case the character could have a Fire focus, which would benefit any spells that were pure Fire or Fire+Summer, but not spells that were 'pure' Summer.