No you cannot do it online. You need to go to an immigration office.
You do not get to pick and choose your immigration office. You must go to the immigration office that matches the province where you are staying, as that is where your TM30 should be filed. That being said, Chiang Mai does in fact have 2 offices where you can apply for a tourist extension. One is the main office near the airport and I believe the other is at central festival mall.
In Chiang Mai you can apply for an extension 45 days in advance.
You cannot activate a visa inside Thailand. The only way to activate a visa is to hand it to the immigration officer along with your passport when you're entering Thailand.
Single entry visas are valid for entry for 90 days from the day they are issued by the embassy. The date you must enter by will be written on your visa.
Until they tell you that you can't. There is no rule that says how many times you can enter as a tourist. It's 100% at the discretion of the immigration officer you are standing in front of. It might be 2 times until they deny you entry, it might be 5 times.
But the fact is you cannot live in Thailand without a long term visa and they have been cracking down hard since visa exempt became 60 days. More and more people have been being pulled out of line and questioned and more people are being denied entry for abusing tourist entries.
For 99.9% of people you'll just need your passport and your boarding pass for your final segment to Thailand. Hand those to the immigration officer and you'll get your entry stamp.
You don't have any visa, so you can't get another one. If you want more time you must leave Thailand and return and you can get a new visa exempt stamp.