Well, yes:
Following the links in the responses to the above topic will give you at least 4 examples to get it done (for uplinks), but all need intermediate servers. That’s all there is to say.
That might very well be possible, but within TTN Console the HTTP Integration has no configuration for “a downlink URL”. Instead, to schedule a new downlink the integration supplies a downlink URL in the payload of whatever URL is triggered for an uplink. (Also visible in your screenshot. Aside: note that invoking that URL might only yield a downlink after the next uplink; see My application’s downlink is always queued for next uplink.) Adding the HTTP integration to a single application multiple times, will make all of them be triggered for each uplink, and using the very same details.
Within TTN, the HTTP Integration is not triggered for a downlink.
If you need something triggered at Thinger.IO when a downlink happens (so: when a downlink is scheduled, and/or when it’s transmitted), then you’ll need an intermediate server that subscribes to events of the MQTT API. However, those MQTT events are only notifications; they do not schedule a downlink if that’s what you’re after.