The real estate company is the payee, and they should be more anxious than you. Push again.

3. I bought a commercial house, paid the down payment and moved in, but I never signed a contract or paid back the loan. ...

Hello, you can ask the developer to sign the contract in time and actually perform it.

4. I paid the down payment, but I haven't signed it online yet. Is it necessary to repay the loan?

Under normal circumstances, after signing the contract, the next step is online signing, then filing, and then loan processing. You can't get a loan without an online sign. But in one case, after paying the down payment, you go directly to apply for a loan to repay the mortgage. At this time, you should pay attention to the fact that the house does not belong to you legally. In addition, the down payment must be signed within the specified time, and if it exceeds, it will be fined.