I have to turn my shower mixing valve much further than usual to get hot water. Also, when i tried to drain the tank, white grit is clogging the drain valve.

Probably the mixer internals are getting stuck. Try dismantling and cleaning it up. This video will help you

There is a "sacrificial anode" inside of a hot water tank, electric or gas-fired. Its purpose is to corrode at a high rate, in order to protect the rest of the heater from corrosion,

All hot water tanks (save the plastic ones)corrode. It is a given,

The sacrificial anode is usually made of zinc, or a zinc/copper/other alloy. When it gets eaten away from electrolysis (the action of minerals in the water, and the metals components of the hot water tank/heating elements/etc make the entire unit operate as a small battery), it usually turns a nasty, crumbly black.

It will leach into the water, and if enough chunks fall off the anode, it will color the water as you describe.

The SOLUTION, to "FixYa", is to write down the model number of your hot water tank, go to the local Home Improvement store (or Amazon.com) and order a new anode. Replacing it is pretty straight-forward: turn off the water, turn off the heater, drain the tank down a bit from a faucet that is lower than the top of the tank (or the valve at the bottom of the tank) , remove and replace the old anode with the new one (it screws into the top of the tank, and is a large-headed "bolt", maybe an inch-and-a-quarter across).

Now that I have written this tremendous missive, I re-read your question/problem and see I missed the mark.

You have "black water" backing up into your shower.

You've plugged your sewer line a bit. Quit using so much toilet paper, you have a near-stoppage of your line. Pour a bottle of Liquid Plumber (or two) down the shower floor drain, let it sit for a number of hours, and then run hot water down the drain at as fast a rate as you can before it starts backing up to clear the clog.

Your use of the term "black water" makes me think you might be in a RV (Recreational Vehicle) or the like, so your problem may be cold-weather related. A heat-gun or hair-dryer ran along the drain lines (or a big heater aimed under the RV for a while) might unfreeze the clog and allow it to pass into the holding tank or sewer line.

Your "Black Water Tank" may simply need to be emptied, too.

Flush more often (important!), use less paper in each flush, eat less beans, and try to p**p in the RV public restrooms more.

Even so, if your are in an RV, the sacrificial anode in your hot water tank is good for only two years, tops, before it fails and your very expensive hot-water tank starts to leak. Fix it anyway.

turn off gas
turn off cold water to heater
connect hose to spickot
place hose end outside
turn on spickot
open hot water faucets in house
wait.
when water stops, turn on cold water for 30-60 sec or so to try to stir up any sentiment in tank
turn off cold water and let drain.
close spickot
turn on cold water
let fill till water start coming out hot water faucets then turn off hot water faucets.
turn on gas and relight pilot.
finish bleeding air from hot water faucets.
set water heater thermostat

Check two things, 1- check that the hot water heater bypass valve is completely closed so that it is not bypassing at all and mixing cold water . 2- check your outside shower valves, make sure both of those are turned off...if they are turned on but the valve on the head is turned off...this will also allow cold water to mix in the hot water line. If those check out ok...then the mixing valve is likely clogged, you could take it off and try soaking it in boiling white vinegar, or try to adjust it, there is an adjustment screw under the black cap, I think its an allen screw...but they fill the center with glue so you can't adjust it...you have to dig that glue out so you can get the allen wrench in...may even be a torx screw...either way it can be adjusted, you just have to dig the glue out first.

Valve is not identified.
Cold water shut-off valve, TP valve, check valve, mixing valve, drain valve are the usual suspects associated with electric water heater.
Gas water heater has additional valves: gas shut off valve and gas control valve thermostat.
Check valve, TP valve and mixing valve probably need replacement.
If drain valve is leaking, put garden hose cap over end.
Shut off valve probably has a bit of blockage, or is not completely open. Try closing and then opening shut-off valve all the way, and if problem persists, replace or clean out valve.

What kind of noise? Are you sure the noise is from a valve or is it inside the tank caused by sediment build-up inside of tank?

http://waterheatertimer.org/Clean-sediment-out-of-water-heater.html
http://waterheatertimer.org/Low-hot-water-pressure.html
http://waterheatertimer.org/How-to-replace-TP-valve.html
http://waterheatertimer.org/images/Water-heater-with-mixing-valve-300.jpg

Have you tried it with both (hot rod and Gas ) turned on at same time? Is tank well insulated? (looking from behind tank.)
Does temperature drop off quickly, or gradually? Did it supply hot water better before, or this is first time you really measured it out? Need to keep in mind that as hot goes out the top fitting to hot lines, cold is coming in the bottom fitting and beginning to mix with hot, which obvioulsy will cause hot to gradually become warm as it enters. 2 gallons out hot tap, 2 gals., at bottom of tank, then mixing as it flows in usually equals, about 2 gal or less of warm, then cold again. Get many complaints of only enough for a short shower when they have 6 gal tank. You can try adjusting temperature up a little to see if it helps. Keep an eye on pressure relief valve dripping excessively as well as shut pump off for 20min-30 min, then turn it back on before touching any taps, to see if it cycles at all, indicating a leak in the system. If pump doesn't cycle when turned back on, no leaks.

The thermostatic mixing spool cartridge may be worn out. The low water pressure may indicate sediment in the cartridge as well. This can be easily removed by hand tools

Not sure but check the inlet water at the heater, the filter may be clog up a little that restrict the flow. Did u use the heater at all during the winter? If not, the heat exchanger may be clogged with built up in there. U need to descale it. Good luck. Chinhcu

Begin by turning off the gas at the tank and at the valve near the tank. CAUTION: Do not proceed any further if you do not know how to relight the gas pilot!
2) Turn off the COLD water supply to the tank.
3) Attach a garden hose to the drain valve at the bottom of the tank. Run the hose to a convenient drain location. Be careful if you use a real cheapy garden hose... some of these become very soft when hot water runs through them, and may leak! If you don't have a drain in the basement floor or suitable sump hole, you have my sympathies... this drain-down can take a while with a bucket! Oh... and be careful if you use a soft plastic bucket. It can also soften from the heated water so don't overfill it or burn yourself!
4) Open up the hot water side of any faucet. Open up the drain valve on the tank and allow it to empty. Miller time. That is, unless you don't have a sump...
NOTE: If the drain valve clogs, turn on the cold water supply to the tank to use water pressure to "blast" through the clog.
5) When the tank is empty, shut off the drain valve and turn on the cold water. This will loosen up more sediment in the tank through the churning action of the cold water in the tank. Let the tank fill partially and drain it again. In fact, if you find that the sediment starts to clog the drain valve, turn on the cold water supply to the tank, which will help loosen the sediment and blast it out.
If you have extreme amounts of sediment, you may have to repeat this procedure a few more times. Look at the drain water... if it is running clear, you are done. Shut off the drain valve, open the cold water supply and allow the tank to fill. Once water comes out of the hot water faucet, the tank is full and your task is done! Now, you can turn the electricity or gas back on to heat the water.
How frequently to clean the sediment from your tank...
This depends on the source and purity of your water supply. Some pros recommend doing it annually, some every few years. I would recommend doing a partial drain down annually if you find any sediment in the tank, otherwise every couple of years.
Remember that with an electric water heater, you must turn the power off! Even a partial drain down may expose the upper heating element to the air and permanently damage it!