Hi.
Your question looks like it can go in growies>composting, but here is as good as any.
I don't use an open barrel, but I do have a closed one. Reason is my climate is semi-arid and water is scarce, so I need the compost 'pile' to be covered with a lid to prevent evaporation and rats.
When you compost in a barrel, it doesn't achieve the high temperatures of a hot compost (70ºC). This means that your weed seeds and maybe some potential diseases are not dealed with. Cold compost is not bad, if you know what you have in hand.
We do not have
enough composting material to make a hot compost, so we only make vermicompost and cold compost in a barrel.
We work it this way:
Since we may be adding materials that can be damaging for the worms, we first put our waste in the barrel. When the barrel is half full and the composting material is almost done, we pour the content into the worms bath tub, just after extracting some worm manure.
For once, I think that feeding almost composted material to the worms is safer for them, and also, using worm manure is safer for our plants than simple cold compost.
No, we don't manage compost teas, we just let the liquids fall to the ground. We lack the manpower to manage this.