Whether you need a new TM30 receipt for every entry to the province is
Provincial immigration office policy.
Some require every time after arrival internationally, some want you to submit even after inter-province travel, while some don't require at all as long as you are back to the same address.
When you travel inside Thailand, usually, accommodations will do your TM30 in that area.
Check with them about their policy when you go to the local immigration office to get the latest requirements handout.
Whether you can do TM30 on your own is between you and your landlord, meaning whether she/he would provide enough documents or not.
Seems like the TM47 system is having trouble and is currently under maintenance. Please wait for a while and try again later. Or contact your local immigration office.