account 吾識分assets同capital

Firms could be a sole proprietoryship or partnership. In your case, it is a sole proprietoryship. For accounting, you should look at the transactions from the point of the firm ( just like a 'person'). You are recording the transactions to reflect the assets ( owned by the firm ) and liabilities ( owed by the firm to proprietor/creditors ), income and expenses of the firm.
1. another $500 cash into the firm. The assets of the firm ( Cash ) has been increased by $500 and there must be a proportionate increase the liabilites as well. In this case, Capital ( for capital injection ) or Sole Proprietor's Current Account ( for working capital funds ) has to be credited where appropriate.
Whenever there is an increase in assets, there must be an increase in liabilities. So, your answer that cash ↑$500 , debtors↑$500 is incorrect. In this case, the proprietor is a 'creditor' of the firm.
By the same argument, the $10,000 paid in by the proprietor, you have to Dr. Bank Account and Cr. Capital Capital ( for capital injection ) or Cr. Sole Proprietor's Current Account ( for working capital funds ) where appropriate.

Answer: 1) cash↑$500
capital ↑$500
2)creditor ↑$200
cash ↑$200

The owner introduced $10000 and deposited the amount into the business
bank account:
bank↑$10000
Capital ↑$10000

你要記住你的身份是公司, 不是owner
見到firm 的話, capital 都要增加
proprietor都可以解作owner

assets 是公司擁有的資產
capital 是owner 給公司的錢