Flexible PE gas pipe is the only cost effective way to go 100'. It is yellow polyethylene and made just for underground nat. and LP gas. This pipe is very cheap compared to copper, but the compression fittings can be expensive. The cheaper fusion fittings require an expensive tool to make a connection. I used the fusion fittings and hired a plumber with the tool to come make the connections after I had the pipe in the ground. So the answer is, yes, you can install a flexible gas line.
Depth requirements vary, since you will need a permit, the ahj can tell you what they require.
For a 15' patio you can wash a hole under it. A 20' stick of 1/2" or 3/4" pvc with a garden hose sweeper nozzle on the end has worked well for me in the past, but I have never washed over about 10'. Success depends on how rocky the soil is.
Also, for that distance, you would probably need a two stage system, with a high pressure regulator at the tank, then a low pressure regulator at the generator.
If there is a place for a second tank closer to the generator, that may be a easier option. Tank rental or purchase is another decision affecting long term cost.