I don’t believe that particular controller for the LED strip would work. It’s wifi and if you wanted to integrate with ST you’d probably need custom firmware for it. There are models out there with custom firmware built that integrates with SmartThings. Just search the forum for RGBW strip.
If you’re looking for a tablet solution, I would check out Action Tiles. You have to pay for it but it’s well worth the money. They host it for you, provide all the templates…it really is a breeze. There are other solutions out there where you run your own website locally. So, depending on how tech savvy you are, you might want to look at one of those. Personally, I’d stick with ActionTiles.
For your downlights, you don’t mention whether you want to have a 3-way switch setup for local control or a single switch. In either case, I wouldn’t go with the nano dimmer, I’d just go with a standard dimming switch. #1 they are a lot cheaper. And #2, if you’re wiring for a 3 way switch, they are a lot simpler. There are several good ones out there. There are a TON of articles up on the forum about the bulb vs switch debate and tons of reviews for switches.