no not anymore decades ago you were able to register at the local police station, but now unfortunately you have to make the trek to immigration or you can possibly do the TM30 as they have a online registration system now.
If you spend 90 consecutive days in Thailand you will need to report to immigration, the only visa at this stage that doesn’t require it is the LTR. But if in doubt go to your local immigration office and ask them.
You will not get a 30 day extension straight away, ask you local immigration office most will let you do a extension with 30 days left on your stamp some will do it with 45 days left. You will have to pay 1,900 baht and some offices will require a copy of your current TM30. So best to ask your local office exactly what their requirements are.