My Mirage (1994, 4G13 (carb), ~95,000km) shudders whenever I accelerate. This is largely a recent problem. This generally occurs after ~2min of driving and persists for ~20 minutes. Depressing the throttle does accelerate the car, albeit very slowly in phases of no power and power. It judders about like a clutch would if it wasn't engaged very well. After it stops the car runs fine. This only occurs when the pedal is further depressed, it can handle static loads fine. The first time this occurred it stalled on takeoff from an intersection (but not the initial start). Here are more probably related (but more historic) problems:
On first run to more than crawling speed depressing the pedal doesn't do much until it quickly speeds up
Car doesn't start (or takes a long time to) if it is parked pointing uphill or with the left side higher than the right (the fuel pump + carb is on the left)
Burns oil on start-up (enough to need to refill it after ~4 months)
Driving up a steep hill (~12%) I could sustain speed (~70Km/h) until I caught up to a bus, so I slowed down and as the road flattened out the bus pulled away and with my foot on the floor I wasn't accelerating at all (similar to point 1)
When low on fuel on two occasions the car has run for ~3 seconds after turning it off
I just replaced the fuel filter and oil, those are not the problems, nor is the air filter, that is reasonably new. Looking down the carb reveals grime but nothing excessive, just thin grease or a thin baked on layer.
What is wrong, I'm 99% sure it's fuel related so carb or fuel pump?