1) How big of an inverter will you need?
First you will have to determine the total wattage of the devices you want to operate. Check the back of the product or manual of your device. Once you find the total watts used, find an inverter that supplies at least that wattage constantly. Inverters have two ratings, a constant and peak rating. For example a 1000w inverter will supply a constant supply of up to 1000 watts but will deliver a peak of 2000 watts. The peak voltage can't be sustained very long but it will allow extra power to start an electric motor or compressor.
If you know the amps of a device and need to convert that to watts, use this formula: Amps x Volts = Watts. For example, a 3 amp motor running on 110 volts AC would convert to 330 watts. You would need an inverter that supplies at least 330 watts constantly. Be sure to allow a slight variance just to be sure.
2) How long will my battery power supply last before it goes dead?
That depends on a lot of variables such as the state of your battery and the amount of power you use. The heavier the load, the fast it will drain your battery. Experimenting with your setup is the best way to determine what you will need to do.
If your battery supply dies too soon for your desired application, you can take one of the following steps to extend your operating time:
Start your vehicle engine for 10 to 15 minutes to recharge the battery or just keep it running while you are using the inverter. Use your volt meter to keep an eye on the battery level.
Attach several batteries together in parallel.
Attach a charger to your battery source.
3) Will it switch automatically from AC to DC when the power goes off?
No. Inverters do not switch automatically however if you have an unreliable AC source, you can run your devices from the inverter all the time. The inverter would be connected to your battery and a charger would also be connected to keep the battery fully charged. If the power goes off, you will be operating from the battery alone and it will slowly use its power and begin to drain down. Once the power comes back on, the charger starts to bring the battery up to its fully charged state. The trick is to have enough battery power to sustain your expected outage time. You can connect multiple batteries together in parallel to extend the run time. A solar panel can also be used to charge the battery bank. All the details are covered in the manual.
The other way to handle it would be to manually switch to DC if your AC power goes off unexpectedly.
4) Does the inverter come with it's own cables?
The smaller inverters come with cables but the larger inverters do not but are available.
5) Will the inverter interfere with my TV or radio?
Inverters use a filtered modified sine wave which eliminates interference.