Close. The water flows down from the DT, through the gate valve (which is open enough to allow the same volume of water that the pump is returning) and into the sump tank. Often times, the first thing in the sump is the filter socks (or equivalent), yes. Then it will often empty into a large area of the sump where the skimmer (which often has it's own pump running) sits. The refugium (or "fuge" for short, though the dictionary on my browser seems to recognize neither...) may - or may not - be part of the that area. It may also be before or after the skimmer (after seems to be common, though it varies). The fuge, by the way, is just a smaller tank with lots of stuff in it that bacteria likes to grow on, stuff that extracts nutrients (algae of some type), or both. So it's a tank in a tank, in effect. Probes and heaters will often be in the large area as well. From that large area, the water will generally flow into another section where the pump returns the water up to the DT.
Dosing pumps are small - very small. They are almost always peristaltic pumps. These pumps draw a small, controlled volume from one area and into another. They do this via "drip lines" - which are just small diameter tubing. The rate of flow is so low through these lines that they just drip out the liquid; thus the term "drip line". These dosing pumps are programmed to only add (relatively) small volumes into the system - often measured in milliliters - at specific times during the day. They are not part of the closed-loop DT-sump-DT system. Instead, they draw from a separate canister (or several canisters - I have 8, for example) that each contain a specific thing to be added to the tank in specific measures. Dosing in "2 part" (one liquid that increases alkalinity and another that does calcium) is likely the most common, but all sorts of additives exist and are added in via dosing pumps. Again; you could do this by hand, of course, but that becomes tedious and error-prone over time.
There are all sorts of ATO's these days, but the most basic is a simple "gravity fed" system. This involves a separate container (tank, bucket, etc.) that holds RO/DI water (and sometimes more) hooked up to a small hose. That hose connects to a float valve. When the water level in the sump drops (due to evaporation, for example), the float opens and RO/DI waters is added in. This brings the water level back up, which closes the float. The result is the same as if you drew a line on your tank to measure it's "full" level and just poured in RO/DI water every day to keep it there - except that it happens constantly and is - again - less tedious and error prone. All you have to worry about is filling the ATO container every so often.
Every sump design is different, but they are not pipes - they are tanks. @saltyfilmfolks Google search link above contains good examples (I just like to type a lot. <grin>).
