If you have 240V equipment from Europe can you use a 240V line to create standard household plugs that run at 240V if you are in North America?

No. This can lead to dangerous results. First, it violates electrical codes to use higher than standard US voltage for portable appliances. There is a much greater risk of fire because the appliances will not be protected by the types and ratings of circuit breakers typical in Europe. Also, the electrical frequency in Europe is different than that in the US (50 vs 60 Hertz). This would affect performance of many appliances and can result in overheating. There are other technical details that have potential for trouble (including electric shock hazard depending upon what type of equipment you had hoped to use). So, stay safe and don't use the European equipment in the US.

I have run 220v 20A connections throughout my house with European Schukostecker -- Euroean outlets -- and the appliances run fine without issue. I have plugged in lamps, hairdryers, toaster ovens, printers, etc. to this connection.

If the amperage on the line gets too high, the breaker will break.

If you do install 220V outlets make sure you use correct wire and breaker sizes. Do not oversize breakers by using an existing oven or dryer circuit, this is very dangerous!! You can purchase 220V breakers of all sizes here, use the correct one. I would also recomment using US 220V outlets and not European outlets as the European outlets are not underwritten in this country and that may cause your house to fail an inspection. You can buy 15A 220V outlets at most home centers here that meet US safety requirements. Then if you need European outlets use some European powerstrips with a US plug installed. Again, use US equipment to install in your home. What you plug into it is your decision.