Is polarity important when connecting electrical wires?

The adapters are called cord caps. These are standard in North America. When you open the cap and access the connection points there are 3 screws. Green is the ground or bare wire, the white goes to the silver screw, the black to the brass colored screw. Follow that color sequence and you should have no problems. This applies only if the pump is 120 volt. If it is a well supply pump it may be 240 volt and you need special cord caps and then only the ground is critical. Since you are in doubt about the electrical work, contact a qualified professional electrician in your area to do the work if you still have problems.

If you are planning on powering the house from the generator with the panel main breaker open (disconnected from the utility) the phasing will not make any difference on a single phase system.

If there is a possibility that the generator will back feed an energized panel then phasing is critical. This second setup is called "paralleling with the utility" and requires specialized paralleling switch gear.

If the system parallels with the utility while out of phase it will cause a massive current draw and result in extensive damage.

I agree with the last post. Better call a local specialist for advice. Someone who can look at the system who has emergency power backup system experience.

After rereading your post it looks like you want to disconnect the pump from the utility and provide power exclusively from the gen set. Under these circumstances the polarity of the phases will not make any difference in pump operation. A single phase 230 volt pump is not de-pendant on phasing. Make sure all grounds, fusing and method of disconnect are in place. Don't connect the pump before the gen reaches rated speed and voltage.

Safety first

Polarity is important sometimes, not in others.

If you wire a DC motor backwards, it will go backwards.

If you wire a DC car radio backwards, it will probably blow a fuse or die.

If you wire an incandescent lamp (AC or DC) backwards, no problem. Except that in the US with screw fittings the centre stud is supposed to be live and the shell neutral so that if you touch the lamp shell you won't get a shock.

With an AC 1-phase or universal motor, like your pump or an electric drill, it should not make any difference. Except that it may have a switch somewhere in the live wire. Newer models tend to have both wires switched.

It is of course important not to get the ground and live wires crossed over (but it would not run). Crossing the ground and neutral is unsafe. It would run, maybe, but that would inject voltage into the ground all through the house and cause your TV and other electronics to hum like crazy, maybe die. Also maybe promote galvanic corrosion in your dishwasher and give you tingles from the water tap.

As for connecting wires correctly, normally they are coloured or have a ridge along one wire. Generally there are standard colours in each country for live, neutral and ground and if you don't follow the rules it will confuse the heck out of anyone doing repairs later and maybe cause them to make unsafe connections.

I can't see why you would be using unmarked wires, but if you are, you could use a meter and another length of wire to check continuity end-to-end after you are done to make sure it is the right way around.

The cables are colour coded for a specific reason. If you don't understand that then for your own safety and that of others call in a qualified person. You could cause a short and also cut short your life. Get a professional in to sort it out.

yes VERY IMPORTANT you could kill yourself using equipment with reversed polarity