You won't care about their website, or their search engine, or their Social Media stuff - listen for what they know about the business. 

I am a Canadian working in California on a TN (NAFTA) visa that will soon turn into a green card but I don't want to miss out on a deal if one presents itself.

Then hope for one of three outcomes (1) the Government passes a lot lower tax rates or some increased deductions allowing you to “get out of tax jail” (2) social unrest leads to a collapse of the governments ability to levy and collect taxes - like in Italy (3) you die before you run out of write offs, and you purchased a life insurance policy large enough to pay your heirs tax bill.

I am leaning towards saying to accept with them understanding that rent must be a priority to pay each month (it's a month to month lease in a very landlord friendly state so eviction wouldn't be too hard and they would need both first month's rent and security in order to move in- in addition to having electric in their name).There aren't any other qualified potential tenants that have come forward- the place has been "for rent" for months now and we have been getting people lying on the application, criminal records, wrong social security numbers, etc.

I have been running in to people that use social security numbers that indicate multiple people are using them when I run the credit report.

Ready to be social on media! 

And then for salary, it probably has to be a check like we get from corporate America jobs (with Medicare taxes +social security taxes subtracted,  etc?)

We're  tribal and social creatures.

You're not paying taxes on that so it's replacing more income.Your rental income will be taxed at the same rate at normal wages, but you don't pay Social Security or Medicare taxes on it.You (or preferably your CPA) will have to do that math for your own situation, but my quick-and-dirty numbers say you'll pay ~$2300 of taxes on $19k of rental income, but ~$7k of taxes on $19k of wage income.

Post to various popular rental sites including social media.