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My PCs have formed a group pattern some time ago. Recently one of them has had thier group pattern item stollen by an enemy ( Leldrin from Ardanyans Revenge).

What can the enemy do with this item?
Can he harm the PC in question via the item?
Can he harm or effect the other members of the group pattern using this item?

I believe that these group pattern items are minor pattern items and as such I expect that it's link to the PC and the group, although solid, is not hugely powerful.

I understand that King Varalus was killed after someone acquired his pattern item But I suspect that this was either a Major or Core item of his so perhaps his circumstances were different.

Ouch, that hurts! He can tie threads to it to boost his abilities when interacting with the group. Your Pcs should be very worried.

ED3PG Chapter Nine P. 113 - 122
Group rules are towards the end of the chapter. (P. 122 "In Friendly or In Enemy Hands") should answer most of your questions.
Page 119 has a small section on People.

There are other uses that have not been described in rules.

Certain ritual spells can be cast at distant targets if you have a pattern items. The king of thrall was killed using such a spell.

Your party is about to re-roll characters. That's what's about to happen.

Give me some examples of what can be done.

I understand that Varulus is believed to have been killed via a stolen pattern item but in Prelude to war it only says that the Dennerastas used a powerful ritual that required a member of their ranks to remain in casting range of The King. The stolen pattern item was planted on the poor Theran exile in Bartertown. So was the pattern item needed for the ritual or simply for the plant?

The weakest possible use for a pattern item in this situation is to simply give the caster a sizeable bonus to whatever spell she cast on the king.
There are also forms of magic that require an actual item associated with the target (like in Direction Arrow), a pattern item of the target (like Moon Shadow), or a thread connection (this is theoretical I think, but weaving to a pattern item would be sufficient). The pattern item is used, in these cases, as a spell component, just like you need pebbles for Earth Darts. Spell components make it harder to cast a spell practically because you need to acquire the components, but decrease the difficulty to actually cast it. Effectively, maybe you could make a 15th Circle spell that kills the target into a 12th Circle spell that does the same, but requires such an item.
We don't know what was actually used, and it could have been a unique spell, but the above are the most likely reasons for the use of a pattern item.