So I took a look at my passport and realized you get a 30 day stamp on arrival, not 59 days. This can be extended an additional 29 days online or in person. Your second extension will likely have to be done in person as immigration will require you to complete the ACR application. It's possible they offer this online too, I just don't know.
Yes, it's an ID card which is required for stays beyond 59 days. In my case I was told to come back to immigration in 4 weeks to pick up the card as they are made in, and shipped from, Manila.
No, you're extending the permission to stay, which I guess is technically the stamp you receive in your passport (visa-free permission to enter and stay for so many days based on nationality). The receipt is your proof of extension (an email if done online). No additional stamps in your passport. You'll only receive additional stamps upon entry to the country. The date of entry on your most recent stamp is what your foreign drivers license validity is based on (you can legally drive with a foreign license for up to 3 months from date of entry).
The card is just an ID card which expires after 1 year. If you leave the country and return, even multiple times, the card is still valid until the expiration date on the back.
I don't know if immigration looks into anything beyond what they typically look at when issuing the extensions, but I've haven't heard of anyone being denied an ACR ID card after being approved for an extension.
Never been there and no plans to go, but most of the apartments I see on facebook marketplace are going for around 5k. Condos appear to be going for 10-20k at the low end, with a few exceptions below 10k. I don't know anything about the city so I can't comment on the locations of these units.
Back when I was looking, most condo ads will state their desire for either a 6 month or 1 year minimum term, but everything is negotiable. I don't know what's typical for <10k apartments. If an apartment building has high occupancy with 1 year leases, management will have little motivation to offer a shorter term. Supply and demand. Plenty of apartment and condo ads though, so I imagine you'll be able to find something nice with a 6 month term. Airbnb is also an option, and most owners should be open to bringing the price down to typical rates for long term stays if you reach out to them. Good luck!