What are the diameters of my pipes from tips back

If you tried using a typical 1/2 to 3/8 faucet connector such as https://www.homedepot.com/p/3-8-in-Compression-x-1-2-in-FIP-x-20-in-Braided-Polymer-Faucet-Connector-B1-20A-F/100459572, and it didn't work then ignore this answer, else...

Plumbing pipe size can be misleading due to the fact the pipe diameter is based on outer diameter and the inner diameter varies with wall thickness. To determine standard pipe diameter you measure the outer diameter and subtract 1/8".

The typical 1/2 inch pipe has an outer diameter of 5/8" and like wise a a 1/4" inner diameter pipe is a 3/8". So likely the typical faucet connector is correct. But you may have something unusual so FYI.

You can convert pipe size to gallons per minute of flow by calculating the cross-sectional area of the pipe and making some reasonable assumptions about pipe volume and the rate of flow. Pipe sizing is measured by the internal diameter of the pipe, not the overall outside diameter. Once determined, the overall volume can be calculated. Pipe flow is described in gallons per minute. Shorter lengths of pipe will have a greater flow than a longer length of the same diameter. This is caused by internal resistance of the pipe itself. By the same reasoning a larger diameter pipe will have a greater flow or GPM than a smaller pipe at the same pressure or flow rate. Pressure is described as pounds per square inch. The square-inch measurement is determined by the area of the pipe. The pounds are the amount of force that is placed on the liquid to push it through the enclosed space.With that background, you can estimate the flow based on the pipe size.
Find the cross-section area of the pipe. Area is equal to pi times the radius squared or a = 3.14 x r2. A two-inch diameter pipe would have a cross-section area of 3.14 x 12 or 3.14 square inches.
Understand that water has a certain pressure associated with the height of that water. One pound of water pressure, or 1 PSI, is equal to 2.31 feet of elevation in height. In other words, a 1-inch column or pipe of water that is 2.31 feet high will have a pressure of 1 PSI. The overall height -- not volume -- of the pipe corresponds to the pressure. A 6-inch diameter pipe that is 2.31 feet high will only have 1 PSI.
Find the volume of the 2-inch diameter pipe in Step 1 that has a length of 10 feet. Ten feet is equal to 120 inches. Multiply 3.14 square inches, the cross sectional area, times the length. The volume of the pipe is equal to 376.8 cubic inches of volume.
Convert cubic inches into cubic feet. One cubic foot equals 1,728 cubic inches. Divide 376.8 cubic inches by 1,728 cubic inches per cubic foot and the answer is .218 cubic feet. This means that the 2-inch diameter pipe that is 10 feet long has an internal volume of .218 cubic feet.
Calculate the amount of water that can be contained in the section of pipe at any given time. One cubic foot of water is equal to 7.48 gallons. Multiply 7.48 gallons by .218 cubic feet and the amount of water in the pipe is equal to 1.63 gallons.
Find the GPM if the flow of water is one foot per second. Multiply the one-foot per second flow by 60 seconds per minute and the flow is now 60 feet per minute. In other words the water will flow through the 10-foot pipe six full volumes for every minute. Since the piping contains 1.63 gallons per 10 feet of pipe, multiply 1.63 by six and the final GPM is equal to 9.78 GPM of water flow from the 2-inch diameter pipe.

The accepted technique for measuring stove pipe is by the inside diameter. Simply because the outside diameter of double and triple wall pipe are much larger by comparison to the inside diameter. There's no standard for outside measurement that would transfer in a logical manner.

You can cut out the Y pipe and replace it with a flex pipe from parts store, then clamp each end of the flex pipe, the pipe diameter will be 1-7/8 or 2 inch, also for the pipe replacement piece would work from a sunfire or cavalier from 1995 and up, might need to replace the muffler strap too. as it can break from rusting, if not already rusted and broken.

A pipe can be seen as two cylinders, one of "air" sitting inside the other, in this case lead.
To get the volume of a pipe you thus subtract the volume of the "air" cylinder from that of the lead cylinder.
Volume of a cylinder = area of circular cross section (or pi times square of the radius) times the height (or length) => ? * r2 * h
Volume of a pipe = Volume of cylinder 1 (outer diameter) - volume of cylinder 2 (inner diameter).

In this case; Volume of outer cylinder => inner diameter 1/2" (0.5") + pipe thickness 1/4" (0.25") = 3/4" (0.75") divided by 2 to get radius = 0.375".
3.14 (?) * 0.375 * 0.375 * 120(10 feet) = 53.01438 in3

Volume of inner cylinder => inner diameter 1/2" (0.5") divided by 2 to get radius = 0.25".
3.14 (?) * 0.25 * 0.25 * 120(10 feet) = 23.56194 in3

Volume of lead in this pipe = 53.01438 - 23.56194 = 29.45244 in3

Hope this helps ;)

If the pipes are 3" outside diameter, the displacement is 24.15 cubic yards, however standard 3" pipe is 3.5" diameter, which would displace 32.85 cubic yards. 505.32 cubic yards is correct for the total trench volume.

3.14 x Diameter x Diameter / 4 x length= Volume in Cubic inches Diameter and Length are in inches.

Multiply the above volume by 0.004 to get gallons.

Did you tip the unit on its side or its back to change the switch? If so, then read on and I may have an idea for you: The water level is controlled by a small pipe that goes into the drum somewhere low down and leads up to a little bellows device (It looks like a spinning top, about 4 inches or so in diameter with a (usually clear plastic) pipe about the thickness of a pencil connected to it and 2 wires. The other end of the pipe is immersed in the water in the tub and as the water rises, so it slightly compresses the air in the pipe, operating the bellows device and throwing a power switch to isolate the water inlet valve. If you have tipped the unit on its side or back, a little water may have got into this pipe. With the water in the pipe, more water is required in the tub before the air in the pipe is compressed enough to operate the bellows. Find the unit, find the pipe, clear out any water in it and the chances are that you fix your problem.

the pump will pump out at a continuos rate that wont change, the problem will be with the standpipe. You dont have to have a total blockage in the pipe, sometimes the diameter of the standpipe reduces due to scale build up and it just cant cope with the rate of flow.There will be a restriction somewhere.