Rock Border around patio-paver pathway - how-to questions...

I am putting in a flag-stone like pathway across my small lawn with patio pavers, bordered by rocks. I have never done this before but I like a challenge. My questions are:

1. Do I put landscape paper under the pavers or should I put the pavers directly on the lawn?
I have tried putting landscape paper under them to prevent weeds from growing through, but the first rainfall has rendered the sand very soupy. The landscape fabric does not seem to allow the water through. We get a severe amount of rain in our region, which is partially why I am converting to a rock-type garden instead of a lawn. I have laid about an inch or so of sand over the fabric and was going to put pea-gravel on top. One thing I did not do was dig out the turf under the stones.

2. Should I dig out the turf under the stones? Do I need to do that?

Another option I thought of was to just put dirt around the stones and plant moss in between them, since moss grows so easily in our climate. If a bit of grass grows through I'm not worried. I just want the end result to be a solid stones pathway, and right now the pavers are wobbling all over the place no matter how much sand I put under them, and the water is pooling on top the sand I put down and turning it to slop. Also, I could put 1" gravel under the stone path, I have a huge supply of that.

Any advice would be welcome. I am working really hard on this but admit I am new to this kind of thing.
I will try to get some pics of this project next time I check in.

I don't get on the internet every day so please be patient if I do not respond immediately.

Thanks!
Jessi