@Ellie Narie Congrats on the househack. I househacked a 4-unit myself in my 20s. I still have it today and it provides great income.
For your first question, let's back up here.
Your depreciable basis is based on what you actually paid for the property; it's the purchase property plus or minus some items on the closing statement as well as any costs you paid outside of escrow that you can include in your basis.
That number is completely independent of what the tax assessor says or what the appraiser says.
When people say to use the assessed value, they're referring to the allocation between land and building.
I think you get this but just want to make sure.
Now, you don't have to use the assessor's allocation if you can come up with some other reasonable allocation.
In my view, using the appraiser's allocation is reasonable. You could also do some more digging...was there a similar plot of land that sold around your property for $100,000 and you paid $400,000 for your property (land and building)? In that case it may be reasonable to allocate 25% land / 75% building.
That said, the IRS likes using the assessor's value and will often challenge other methods. Sometimes they win, and sometimes they lose. There was a Tax Court Summary Opinion a few years back (Nielsen) where the Tax Court sided with the IRS who wanted to use the county assessor's allocation, while the taxpayer depended on alternative methods I described above.
Also keep in mind that because you're living in one of the units, you can't depreciate the entire property for rental income / loss purposes -- only the amount attributable to the portions you're renting out.
As for the points, again, you must allocate between the points allocable to your residence portion of the property and the rental portion of the property. The former are generally amortize as an intangible asset, but you may be able to deduct them in full as prepaid interest in the year you pay them if you meet certain requirements and you itemize deductions. The points allocable to the rental portion should be capitalized as an intangible asset and amortized over the length of the loan.