Looking for 2 15amp single pole pushmatic circuit breakers.

I dont believe there is any difference between a pushmatic main and a pushmatic two pole. These panels came with stickers labeled "MAIN" that were simply applied at the time of installation. Likely you wont find a two pole 30 Amp in stock but it can be ordered.

https://www.menards.com/main/electrical/circuit-protection-power-distribution/circuit-breakers/pushmatic-reg-30-amp-2-pole-type-tb-classified-circuit-breaker/vpkubip230/p-1444427371526-c-1489583170892.htm

I recommend you NOT buy a used pushmatic breaker on eBay or other. There's a reason this type of panel is no longer manufactured.

Some of these numbers don't make sense?
I have Never heard of 440v and 220v in a residential application, they are two different systems, 480 volt is typically 3 phase power, and 240v is typically single phase, more in likely you have a 200- 400 amp main service, and a 100- 200 amp secondary service for the welder, that can't be 110 @ 200 amps?
I would need more info, and pictures of actual nameplates of the equipment,
and then I could advise a safe NEC electrical code answer...

In a traditional North American residential electrical panel (120/240 volt, single phase), installing a single width or single pole circuit breaker, you would expect to read 120 volts from the breaker terminal screw to either ground or neutral. A double width or double pole breaker would provide 120 volts from either of the breaker terminal screws to ground or neutral AND it will provide 240 volts BETWEEN the TWO breaker terminals.

A single-width circuit breaker case that contains two handles is NOT a two pole circuit breaker (these are called "tandem" or "1/2 size" breakers). This is because a single width breaker engages only one "line" in the panel. A double width breaker will engage 2 "lines" as a triple width breaker would engage 3 "lines" of a 3 phase panel. A single wide breaker can not physically engage more than 1 "line" so it will never be able to pass 240 volts.

You must install a double width / double pole breaker to safely supply a 240 volt circuit / device.

Yes. A two-pole breaker is just two breakers hooked together. But the very important part is that if one pole trips THEY MUST BOTH TRIP. If only one trips, then the circuit won't operate the appliance (whatever it is) but one of the poles will still be live!

You need 240 breaker:
Notice that your 240V breaker is twice as wide as regular 120V breaker.
Notice that both switches are tied together on 240V breaker, making this a double-pole breaker.
For more information about breakers and 120-240V circuits:
http://waterheatertimer.org/See-inside-main-breaker-box.html
http://waterheatertimer.org/B220C.html

You are correct. Try replacing the single pole breakers with thinner space saver breakers to get more space in the pannel.

You have it shorted out somewhere along the line. If it is a light switch you are switching, what have you done lately to make this trip? Anything? You might have a bad breaker. You can check it by shutting off the power, pull the wire out of the tripping breaker, put it in another breaker, turn the power back on, switch the breaker on, then hit the switch and see what happens. If it snaps off, it is not the breaker, but the switch, the wires in the box, or the lights, or something along the line, you will have to check each one. New construction has made all lights and all receptacles separate, so if your house is old, you might be looking at receptacles too. Check anything plugged in to an outlet, make sure there is nothing shorting. Hope this helps.

Most two-pole breakers have a small plastic bar that connects the two switches allowing them to be synchronized and used as a single breaker. However there are some two pole breakers that are intended to be used as two separate breaker and lack the need for the bar that synchronizes them, this is because they are not being used to power a single circuit or item, but separate circuits, or items. so no the breaker is not bad, and yes can be used to power single circuits or items.

It could be either or at this point. First thing to do, is unplug all electric devices from the plugs on that circuit, and then attempt to reset the breaker. If it does not trip, one of the devices plugged into a receptacle on that circuit could have a short. If it doesn't trip, plug each device in one at a time to see it it trips the breaker to pin point what is causing the short. If the above has no effect, I recommend replacing the breaker. It is easy and inexpensive to do. Just make sure you main is shut off before doing any work on the panel. I hope this helps and good luck!

You need to put in what we call a sub box. This should be done by a licensed electrician, but if you really want to do it yourself you will need a distribution box some wire and it has to be connected directly to your main lags from the meter box, this box will have a main breaker built into it and spaces for additional breakers, depending on your existing wiring the electrician might chose to wire the additional box directly to your meter base and not your existing box. Either way you really should seek local professional help on this project, just for your safety and to satisfy your home-owners insurance.

Have a great day..
Tim