So point by point.
So quick questions. Casting a spell in battle such as shatter or paralyze requires battlemage, and thats fine.
You do not need Battlemage to cast Spells in Battle. anyone who knows a spell can cast it at any time if they have Personal or Crystal Mana. Battle mage lets you use Mage armour and Staffs but that is all
I cant find any mention of rituals requiring that in battle, specifically the battle rituals.
Thats because Battle mage is not permission to cast in battle it is options for a battle focused wizard
.Would it then be possible for a heavy armour wearing mage whose a part of a coven to be part of a ritual spell casting if he has the apropriate skills to cast the ritual?
No but that is because ritual casting, or in fact spells as well, do not work while wearing any armour other than mage armour. You can certainly be a ritualist cast your rituals, then put your armour on and go off and fight with a sword.
Assuming one has a wand or a rod of course.
You do not need a Rod or a Wand to cast a ritual only for delivering combat spells, all other rituals or spells can be cast without.