Determining Battery Charging and Discharging Rate Based on Max Current and Nominal Voltage
I am having difficulty in figuring out some basic stuff and confused with multiple equations.

When in difficulty multiply out the units to see if they make sense. We'll see some errors below.

I have already calculated:
How much energy vehicle is regenerating at each braking event in kWh.

Good. Energy = Power x time = kW x h = kWh. This is correct.

Battery specifications are:
Storage                = 30.6 kWh or 46 Ah

So you have assumed that battery voltage = \$ \frac {P}{I} = \frac {30.6k}{46} = 665\ \text V \$. That's fine.

Max Peak Power         = 406 kW for 10 Sec

OK, but let's use 's' for seconds as in the SI standard units.

Continuous Power (RMS) = 77 kW

RMS is supposed to be used to find the equivalent DC voltage or current for a voltage or current waveform. It doesn't make sense in power measurements as the average is what is required.

Voltage                = Nominal = 666 V, min = 486 V, max = 756 V

OK. Add a space between the numbers and the units for clarity. e.g., &quot;6 cars&quot;, not &quot;6cars&quot;. This is recommended in the SI standard. No spaces before commas.

Battery Rating        = 6C
Battery max Charge / max Discharge Rate per hour = 6C * 46 Ah = 276 A

Here you're a little mixed up again. The ampere already is a rate measurement. It's the amount of charge (coulombs) per second. &quot;Discharge rate per hour&quot; doesn't make sense. Just say &quot;max discharge rate = 276 A&quot;.
But now we see a problem. 276 A is the 6C rate which means that it will be all over (charging or discharging) in 1/6 hours = 10 minutes.

How can I calculate how much maximum energy my battery can absorb?

The battery can only absorb the amount of energy required to fully charge it from its current state + losses due to heat.
I'm not a battery expert but I would expect that the maximum charge rate would be close to the maximum discharge rate.

So in my algorithm I can automate the code to send only the amount of energy which battery can absorb for such given period of time and destroy rest in brake resistors.

That seems fair.

Energy = Power Time = Voltage x Current x 1 Hour

Make that &quot;power x time&quot; and that is correct if you sustain it for one hour.

Energy = 666 x 276 x 1 = 183816 Wh

That's 183 kWh but at the start of the question you had calculated the actual capacity at 30.6 kWh. Your 1 hour needs to be divided by 6.

Energy = 183816 /60/60 = 51.06 Wsec

No, if you are converting Wh to Ws then you would multiply by 3600. So energy = 183 kWh = 183k x 3600 = 659 MWs (MJ, megajoules). (But don't forget that 183 kWh is wrong to start with.)

So the battery can absorb 0.05106 kW per second

No, kW/s is nonsense.
As @jonk has suggested, hit the edit link under your question, clean it up taking care with your numbers and units and then ask the question at the end.

Update after edit.
I think you're making it more complicated than you need to. Just figure out the charge / discharge power, \$ P = VI = 666 \times 276 = 182484 \ \text W = 180 \ \text {kW} \$ to two significant figures.
Energy transfer rate at this power will be 180 kWs or 180 kJ. (This should make it easy to convert back and forth between electrical and kinetic energy.

Considering this, 3063.6 Wh / 60 sec = 51.06 Wh energy can be charged or discharged from battery at each second at 6C rating.

To convert from kWs to kWh divide by 3600.

Comments:

It's not clear what exactly you're trying to work out.
You seem to assume that you'll be discharging at 180 kW continuously. This seems unlikely for a typical electric vehicle.
Have you worked out what 180 kW of deceleration will feel like on a 1000 kg car?