I imported a number of W123 230E cars into the US in the early and mid 80's, and they each exhibited a sensitivity to high ambient temperatures and fuel pump relay behaviour. To keep the customers satisfied (my sisters and my aunt, as well as a local doctor) I keep two of these relays in "stock" at all times. Their cars would stall or not start and then when AAA arrived it made them look like dopes when the mechanic would get in the car and try it, and it would start. Eventually they stop resetting when they cool off, or rest or whatever the issue is.
The fuel pumps are pretty loud, and if they have been reinstalled without the original sound isolation hardware, they can be very loud. You have to take the pump and its filter down together on the older cars, and I assume the newer ones too, to change the filter (the filter and pump are mounted on a common base plate that is mounted on rubber to the car body). If you put it back so the rubber is either missing, or the solid objects on the base plate are touching the body, or the rubber is squashed too tight, the noise level will increase. They used to be located around the driver side rear wheel.
I am not clear on how to check the fuel pump relay, and on the ones I "stock" the guts are potted in a compound so you cannot really get to the insides very readily. They are not cheap, around $60-90 depending on exchange rates and when you buy them. Good Luck, Jim
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)