Next water change put the suction hose next to the Aptista and while sucking it up use some tweezers to pull it off and let it go up the suction hose. Be sure to grab it as low as possible, and watch out as they sting. After that use some aquarium putty and cover the area it was on with it.
That is the simplest way to remove one insuring no bits go floating off & smother any part that might have been left behind. If you find some on your glass use the suction hose and scrape it off the glass with a razor blade. Be sure to use a new razor blade, I wash mine with soap, then rubbing alcohol, then vinegar, then finally rinse with RO/DI.
The "vines" are rather the feather duster's tubes. They are a tube worm, which live in a calcifies tube the worm creates. The "feather" part you see is actually a food-particle catcher the worm throws out to feed.
And that's how you can tell what things in your pictures are feather dusters and which are Aiptasia; the presence or lack-of of the white tube below them.
Kill the Aiptasia now, before they are a problem. Kalk paste works well.
i've been able to kill aptasia with vinegar...since i dose vinegar daily with a syringe anyway instead of just dosing it onto the water column, i turn off my pumps and blast the aptasia with the vinegar...if they don't die the first time, they die on the 2nd or 3rd time