I understand that in the fuel system of an aircraft, the fuel first go through wobble pumps--manually driven, and then fuel strainers--for filtering out debris, and finally the engine driven pumps. This is the source: https://angf35eis.com/what-are-aircraft-fuel-system-components/. But I am curious of whether we can change the order of things fuel goes through? Can we go through strainers first? Can the fuel go through engine driven pumps first before going through wobble pump?
Wobble pumps are manually operated boost pumps and are normally upstream of the engine driven pump, often used to help prime it by pre-pressurizing the engine pump inlet before starting. The DeHavilland Beaver had a wobble boost pump as the sole backup pump, which you would use to build fuel pressure before starting, and if the engine pump quit, you could keep flying by stroking the wobble pump (down by your right knee) about once every two or three seconds.
You don't see many wobble pumps today; just about all boost pumps are electric.
The location of the filtering elements like strainer units and the pumps isn't that important from the standpoint of fuel delivery to the engine. The strainer location is usually determined by where is the lowest point in the fuel system, because that's where you want water to collect to be drained off.
Both engine driven and boost pumps usually are made with a bypass circuit that allows fuel to get past it if the pump isn't working, pulled or pushed by the backup pump, and neither pump cares too much about where it's actually located as long as the suction side is not obstructed.
That being said, the ideal location for any pump is as close to the tank as possible, so that it's doing a maximum amount of pushing and a minimum amount of,... er, sucking. On most airliners, the boost pumps are right in the tank and pull fuel directly into the pump inlet. This maximizes resistance to vapour lock, by minimizing the fuel exposed to suction-induced pressure drop, which to the fuel is like going up several thousand feet in altitude.
It's also preferable to locate pumps away from heat sources. A lot of GA airplanes put their electric boost pumps in the engine compartment along with the engine driven pump, to minimize plumbing and wiring. Not too big a deal on avgas, but if you operate on Mogas (as I do), which has a lower boiling point and is more prone to vapour lock than avgas, this can become a problem in really hot weather. My plane has its electric boost pump on the front of the firewall, and I'd like to move it to the cockpit, or ideally, to two separate electric pumps right at the fuel tanks. Moving it from downstream to upstream of the gascolator isn't really an issue.