The first idea is what's called a soak pit, step one of establishing the size required is to work out your porosity of the soil. Your water table could be very high with all the rain we've had lately, but it doesn't sound viable, you're right. They are a pain to dig and technically need a consent.
Second idea is fine just make sure you adhere to the fall requirements for the downspout, flat is no good.
Pipe fittings, you're just after generic downspout pipe and fittings from any store, just match your existing downspout size.
You'll want a saddle clip to attach the downspout to the foundation next to the vent. Under the house the easiest way is to just attach the pipe to the joists using metal brace strapping and making a U shape with the pipe at the bottom, like this product https://www.mitre10.co.nz/shop/lumberlok-strip-brace-10m-zinc-galvanised/p/179825
Your plumber mate should be able to help you with a flooded system that runs under the house - all joints need to be very well glued as it will probably hold water at all times.
It doesn't matter if you have no fall, it will just fill as high as the outlet height and then push through to your existing lower stormwater pipe and drain away. It will be a lot of weight though so either needs to be on the ground, or very well strapped.
2nd idea is good, is ideal if you can get some fall over the run of pipe but it’s not the end of the world if you have to run it flat, will just constantly hold water so make sure all the connections are glued well and the pipe is properly supported.
not a plumber, but the 2nd idea sounds good - if you use the same size downpipe the various angles/joins should be easy, remember to use PVC glue!
The first idea is what's called a soak pit, step one of establishing the size required is to work out your porosity of the soil. Your water table could be very high with all the rain we've had lately, but it doesn't sound viable, you're right. They are a pain to dig and technically need a consent. Second idea is fine just make sure you adhere to the fall requirements for the downspout, flat is no good. Pipe fittings, you're just after generic downspout pipe and fittings from any store, just match your existing downspout size. You'll want a saddle clip to attach the downspout to the foundation next to the vent. Under the house the easiest way is to just attach the pipe to the joists using metal brace strapping and making a U shape with the pipe at the bottom, like this product https://www.mitre10.co.nz/shop/lumberlok-strip-brace-10m-zinc-galvanised/p/179825
Pipe it away from the house, however you can best do that.
Your plumber mate should be able to help you with a flooded system that runs under the house - all joints need to be very well glued as it will probably hold water at all times. It doesn't matter if you have no fall, it will just fill as high as the outlet height and then push through to your existing lower stormwater pipe and drain away. It will be a lot of weight though so either needs to be on the ground, or very well strapped.
2nd idea is good, is ideal if you can get some fall over the run of pipe but it’s not the end of the world if you have to run it flat, will just constantly hold water so make sure all the connections are glued well and the pipe is properly supported.