Where can I put damages paid in the trial balance?

Where can I put bike repairs in the trial balance?

Where can I put heat and light in the trial balance?

You do not put these things in the Trial Balance.
1) Damages Paid goes in the Cash Receipts
Journal.
2) Bike Repairs is an expense, it goes in
The Expenses Journal.
3) Likewise Heat and Light is also an expense,
It goes in the Expenses Journal.

When all the journals are posted to the ledger,
The ledger accounts with closing balances
Are listed and this list is called the Trial Balance.
Because you are using the double entry system, by definition the totals of the debits and the credits in the Trial Balance must be equal.
This is what tells you that the ledger has been properly posted.

Rolcam, since when the payments are recorded in a cash receipts journal?

I understood the question as damages paid to the firm.
If it is damages paid out to third parties then it goes in the Payments Journal.
The way the questioner put it is not 100% clear.

I'd like to know where the assumption came from that this is even a payments journal rather than a general journal. Not everyone learns the special journals.

fabregas, what exactly do you need to know? Assuming those are all expenses, they belong with the rest of the expenses in the trial balance. That answers "where," which is what you are asking. Otherwise, you need to specify what you mean by "where." The second two don't even specify they were paid, or if they received a bill, so no way to even know for sure what those journal entries are.

In other words, the information and the question are ambiguous and don't gel.