You don't need any written agreements, you'd just want to keep a good track of the transactions in your records. You can do exactly what you intend and lodge money to the company from personal funds and it will be a directors loan. You'll thank yourself down the line if you lodge money to the company and make the loan repayments from the company, much cleaner than making the loan repayments privately and reimbursing at a later date.
The current value of the vehicle would be repayable to you if you brought it into the company in the same way as if you lodged cash to the company. If it's a car then best discuss with your accountant because if BIK applies it can be a killer and its based on the original market value, not the current value. BIK isn't as bad if it is a van but still not great. You may be better off keeping it private and paying mileage from the company