Ritsuka needs to purchase contracts slots to hold contracts. It's 2 points per contract slot, and you can purchase up to 4 of these slots (8 points total).
She hasn't purchased any slots yet, so she cannot form any contracts or use any shadow templates at this time.
Once she purchase contract slots, she will be able to reactivate the contracts at no additional cost to herself as long as she doesn't try to hold more contracts than she currently has slots for. Should a servant she has a contract with drops and another servant apps, she will be able to form a contract with the new servant free of cost as she'll have a slot open.
Any unused slots that she has purchased can be used to summon shadow servants (which are 4 points per shadow servant at base power). But she cannot exceed four, regardless of if they are OU/AU/or shadow servants.
As for Gil, the contract will only reactivate if you and Gilgamesh's player will decide if it reactivates. If yes it'll reactivate, then it'll take up a slot. If you two decide against it, then no it won't take a slot.
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Thank you!