If I am dubious of their documentation, I may ask for bank statements to see deposits.

Then they'll keep your deposit and sell it to someone else if you don't want to buy it.

I ask for a 50% deposit and 50% at completion for jobs under $20k.

I usually charge a $50 deposit per pet and $50/month per pet. 

The Mortgagee must obtain a lease agreement of at least one year’s duration after the Mortgage is closed and evidence of the payment of the security deposit or first month’s rent.

For the month of August 2024, they are saying that they have hardship and want me to use the money they paid as security deposit (2X rent).Legally, am I required to use security deposit towards rent when they are delinquent or can I move forward with eviction process?

It usually starts with a notice being posted, so get that done asap to 'start the clock'.Keep in mind you should receive their security deposit as a transfer from the previous landlord as a part of closing, so that will at least compensate you somewhat for the lost income if they haven't trashed the place and such.One other set of questions would be - do you want them to leave?  

It certainly could improve your cash flow but it won't help with finding prospects, screening tenants, maintenance, deposit dispositions, etc. 

We have just 5 properties, but with turnover each year, it is very time-consuming to figure out security deposit refunds net of any deductions.

(Had a tenant put a deposit down and has taken a month for the PM to put in a fridge and stove. that was paid for a month prior to that).