If I do a Bull Put Spread and hold this till expiry for a stock, does the margin of this strategy increase near expiry?
Currently, the bull put spread shows a margin requirement of just 42k on sensibull.
Its a bit tricky, so for example if both legs go ITM, then you need maximum margin. Even the Buy Leg will require delivery margin on expiry day(50%). Both legs will block almost full value of lot size delivery margin. That too the margin will show in “delivery margin” and the cash component is used up first.
If the legs are OTM more than 3-5 strikes, you will have case of minimal margin, however, margin will most likely increase slightly in expiry week but not very significantly.
This is applicable even for a Covered Strategy like BULL PUT SPREAD, where I am buying one put and selling another?
yes, bcos each leg is treated independently due to delivery risk.
So when legs are 3-5 strikes OTM, then you will just get email/push notifications about physical settlement, but if both legs are ATM/ITM, you will need around 6L on expiry day.
Either way, unless OTM, better to square-off otherwise brokerage etc will be much higher.
see how much margin increases in expiry week here
What is Zerodha’s policy on the physical settlement of equity derivatives on expiry?
This is helpful, thank you 
One more thing, If both legs are OTM on expiry and if I let them expire OTM, does is automatically cash settled? (Meaning, will I simply get the P&L amount, and no extra charges or taxes are applicable, just like Nifty Options) ?
if both are OTM, they expire worthless, so no charges like STT/brokerage etc.