Yes, since it's your 2nd job then it'd require a 2 year history. Doesn't matter the loan program, it's just a guideline that exists throughout the industry. You don't always have to have 2 years doing the same 2nd job, just a 2-year history of working a 2nd job.
But since your 2nd job is self-employment, then in order to use it as a 2nd job you'll need 2 years of the same self-employment. Reason being is most businesses fail within 2 years, so if you have that much history then underwriters assume it's likely to continue.
When using bank statements to qualify you have the option of using personal or business bank statements. The business related deposits in your personal bank statements usually are used at 100%, but with business bank statements they often are given a 50% haircut to account for business expenses (or if your CPA confirms a lower expense factor then that usually can be used).
Further, property taxes in California will almost always be at least 1% of the sales price as that is the basic levy rate for any residential real estate in California. There is a homeowner's exemption that will knock $7k off the assessed value (saves a whopping $70/year in property taxes) but that is the most common exemption. So the $1.2MM sales price will have around $12k/year in taxes, possibly more if there are additional assessments. Most counties here will allow you to search for current property tax bills by entering in the property address and then will allow you to download or view the most recent property tax bill so you can see the tax rates.
For example below is a propery tax breakdown for a home in Orange County. The assessed value of the home started out at 100% of the sales price, plus can increase up to 3% per year (it could also decrease if home values were declining). You can see that the tax rate is 1.0035% of the sales price + flat taxes of another $15.73. If this was the tax bill for a $1.2MM home you were buying then the property taxes would be $11,971.755 + $15.73 = $11,987.485/year or $998.96/mo.
A lot of lenders here in California will just calculate property taxes at 1.25% of the sales price though, so that is a good rule of thumb to use but with documentation you should be able to convince your lender to use the actual property tax rate.
The online calculators that purport to let you know how much you can qualify for can be all over the place, as they can make some inaccurate assumptions. If you are trying to stretch how much you can qualify for then you'll absolutely need to speak with a loan officer and provide any needed documents to get a proper idea.
$235k/year of income with $1,350/mo of debt payments could qualify for a $1.2MM sales price but it'd probably be looking at more like a 10% down payment and using FHA financing to allow a higher debt to income ratio to qualify, plus in the highest cost counties the FHA and conforming loan limit maxes out at a $1,089,300 loan amount. In general, financing above that loan amount would require you to obtain a jumbo loan (usually requires a larger down payment) or you can do a 1st/2nd combo loan, which would still allow 5% down. Either way, the $930k loan amount estimate from Chase appears to be low.
