Electrical – 15 amp load trips 20 amp breaker instantanously

As Isherwood and Ecnerwal advised, it would be in your best interest to set a sub-panel in the garage.

TL:DR Set a 60 amp sub-panel and feed it with #6 NM wire from the main panel. Separate all your neutrals and grounds at the sub-panel and buy the ground bar kit for the ground wires to attach to in the sub-panel. DO NOT install any bonding screws between the box and neutral bar. (If your welder draws more than 20 amps you should probably upsize this to 100 amp panel fed with #3 wire if you plan to have the compressor and welder on at the same time.)

Longer version: The size of the panel depends on what you plan to run now and what you may plan to run in the future. The 2.5 hp compressor is the largest load you listed and will draw a little over 24 amps at according to Table 430.248 of the National Electrical Code. Let's say 28 amps at 120 volts. (Is there any way to re-wire the compressor for 240 volts? This would halve the current and reduce your voltage drop.)

The proper way to size this is 125% of the largest motor's listed current from the Table 248 in the NEC plus 100% of all the other motors table listed currents. Then, take all your other devices and add the current draw on each one at 100%. Take the total and divide it by 2 since you will be running a 240 volt circuit and all the loads are 120 volts and the current is split between the two legs. Now you have your current draw for all loads in the garage and this is the current draw for the feeder to the sub-panel.

For the sake of argument let's say you come up with 40 amps (this may be high or low for what you have listed but you didn't have a current draw for the wire welder so I will press on). You could then run a #8 circuit if the feed was shorter but to compensate for distance and voltage drop you upsize one wire size to #6 wire. Since you can only get sub-panels in certain sizes you will most likely have to buy a 60 amp sub panel without a main breaker in it. (Since the garage is attached through the breezeway you don't have to drive a separate ground rod. So don't worry about that.) If you go with a 100 amp sub because of the draw of the welder then You may end up with the #2 wire to compensate for voltage drop.

Now, unless your local building code requires it (and Chicago is the only place I know that requires Conduit in residential) you don't have to use conduit. You can use standard NM copper cable to make this run and it will be way more affordable than running conduit and pulling wire.

Power factor is not considered when sizing circuits in residential occupancies. End of story.

The number of circuits is a consideration for convenience but is not taken into account when calculating the size of the sub-panel and its corresponding feeders and breaker.

So, there you have it. Simple eh?

A large inductive load, such a motor starting, often causes a ground-fault circuit interrupter to trip even when there is no fault in the device. A snubber, a small capacitor and resistor across the line, can help mitigate the issue. A voltage surge protector can also help, but avoid protectors with large varistors from line to ground, which can also trigger the GFCI.

You might also need a Class C or other type of GFCI which allows greater fault current to flow for a longer time, depending on shop voltage, appliance grounding and insulation.