Having the verandah not level will work in your favour because you need it to be able to drain under the decking.
I have laid a deck over concrete by fixing 1" thick battens to the slab with galvanised masonry anchors and then screwing the decking to that. It required some packing to get it level, but I don't think it is mandatory for a deck to be perfectly level, as long as it looks OK.
Make sure you allow for drainage. Run the battens so that water getting under the deck can flow away easily. I don't think there's any need for a membrane.
If you're going to extend the deck out, you'll need to decide on stump spacing, then we can look up the bearer size you need.
A photo or two would help.
I reckon the main problem with this set up is that you wont be able to access the underside of the deck once it's laid, so anything dropped in the gap will stay there. If it's located under trees, that might cause problems over time, I don't know.
"I don't practice what I preach because I'm not the kind of person I'm preaching to."