Bike Friday make the Pocket Rocket and Pocket Rocket Pro with drops and STI. They use very good quality components like Shimano, Campag and Sram and the build quality is good. The fold is not as small or quick as other brands.
Other companies like Birdy, Swift and even high end Dahons are worth a look, but most come with flat bars, Moulton and Pacific make bikes with drops.

Yes you can use drop ends on flat bars, but there are some issues you need to consider.
1: If you retain the flat bar shifters and brake levers you will not have brake levers on the drops, which if you are a serious roadie might feel odd and might take time to get used to. If I was to to this I would install a set of tandem stoker "dummy" hoods so I could use the extra reach that drops provide.
2: You can change to STI so you can use drops, but if the bike comes with Vbrakes as a lot of Dahons do, you will have use travel agents to get enough "pull" on the brake cable for effective braking.

If you don't need to fold the pedals then clip less are OK.