So would it be ok to directly couple the thin copper wire of the antenna to the RTL SDR SMA inputs ? There is no balun there, so that is why I ask (no experience on RF matters). The antenna would be used indoor.
You really want to keep that USB cable and its traffic away from the antenna. Putting it right next to the antenna feedpoint is a recipe for increased noise… as is mounting the antenna inside your house.
For a 70cm turnstile, you really need a preamplifier as well - signal levels are lower in general, and you need the sensitivity improvement that a preamp gives.