This was incorrect. The account you select on a sales invoice controls where the credit side of the transaction is posted. Since you created and selected an asset account, the amount shows as negative because all asset accounts are debit accounts. See https://www.manager.io/guides/8965 for an explanation.
Yes it did. That asset account you created is a balance sheet account. If it became more negative, you were affecting the balance sheet. The reason the total assets did not change is because the debit to Accounts receivable was offset by the credit to your self-made asset account.
What you should do is select an income account. There, as you have seen, the effect will be positive.
You have not extended loans. You have raised sales invoices, which are demands for payment in return for goods or services delivered. A loan involves the giving of money for use by the other party with the expectation of repayment.
What you just described, @Hosea_Leonard, is the difference between accrual and cash basis accounting. See https://www.manager.io/guides/7129. If you use accrual basis, you have no choice—the invoice must appear in an income account (as a credit) to balance the account receivable (a debit).
You should understand that cash basis reporting still debits and credits amounts the same places. The difference between the two methods lies with when they are reported. Under cash basis accounting, the income will not be reported until you receive payment.
For a business as complex as a hospital, almost any accountant would recommend accrual basis accounting. Your local law may require it. And if customers do not pay their invoices, the proper thing is to write them off as bad debts. See https://www.manager.io/guides/14465. This will result in the loss being shown as an expense, reducing net income.