I was able to test my DC motor on it on 12V power supply.
But as I need to use the 24V power supply and my dc motor is 350w 24v I've asked a seller to send a correct item.
When I've finally received IMS-2C, which I've ordered, I've connected it to my Arduino and DC motor and tried the same simple code as run with IMS-2B, so the code works, sorry, can provide it later.
And controller runs motor for 1-2 seconds and stopped when I reset the Arduino it repeats.
A seller told me that that I should connect V+ pin higher than 5V when I've connected it to 11,6V IMS-2C died.
Also, he told me that I need take controller with current = motor current*3, not sure if it should be so big margin.
So my main question is: which DC motor controller should I use with my 350w 24v DC motor and with Arduino to control motor's direction and speed and also control a current load.
Thank you in advance.
What SureshKumar is describing is an h-bridge. Unfortunately it's tricky to implement for higher currents especially for a 24v motor. It can be done but there will be much more involved than four MOSFETs.
The IMS-2B and IMS-2C are just inexpensive H-bridges; four mosfets and then it adds mosfet drivers for more efficiency and it appears it has a switching regulator to feed those mosfet drivers. Nothing extraordinary but it's obviously much easier to buy a board like this rather than build it yourself.
It's impossible to give a straight answer without a schematic, bit I would not recommend putting more than 5V into that "V+" pin. The seller probably meant that you need more than ~11V into the B+ socket (the motor power) because that switching regulator is likely a buck regulator and needs to be fed a higher voltage than whatever voltage it's outputting.
As to why you're only getting ~2 seconds of runtime is anyone's guess. When you buy these boards from China you get what you pay for; sometimes there's actual quality control happening where the manufacturer tests their boards but more than likely not, and then those times when they do test their boards they probably still sell the defective boards at a discount to any eBay seller that wants them. Buying these things on eBay is like playing in the 2006 mortgage-backed securities market.
Lastly you asked why the seller recommended buying a controller rated at 3 times the current. If you look at the board you have, with four "D-Pak" transistors, that package type of transistor is limited to 30A continuous. The 50A rating is bullshit, but then you should at least thank the seller for not rating it at the 620A peak, pulsed rating of the IR7843 mosfets it's built with.
A thing you have to beware of is stall current - unless you are careful about ramping the PWM level and
sensing current dynamically, you risk pulling upto the stall current from the supply (if it can handle it),
and stall currents are 5 to 10 times motor rated load currents typically - a 350W 24V motor may only have
0.25 ohms of winding resistance, ie could pull 100A at start up, which is bad news if the motor driver cannot
handle this robustly.
The reason this current is so high is so that the motor losses are reasonable at normal running load, which is
14A or so - 0.25 ohms at 14A is about 50W of dissipation in the windings, ie 1/7th of the input power... Make
the winding resistance higher and the motor runs hotter (and the stall current is less).