Only going by the description of what you wrote down, and the knowledge that the car still does not run on its own.
It is clear you have two problems at least.
First the slipping transmission in 2nd gear and the sticking clutch pedal.
You cannot tell me that this problem has resolved itself when the car is not running.
The fact that it will start with starting fluid or whatever you used to spray into the intake tells me you have a lack of fuel. this does not mean the fuel pump is bad.
This just means you need to diagnose the no start problem. the lack of fuel could be no power to the pump or no reference pulse to the injectors and yes it also could be a bad pump.
This forum and many others that I frequent are littered with people that buy parts, hang them on the car cross their fingers and hope the money they tossed at the car fixes the problem.
A handful of people get lucky doing this yet the smart ones, the ones that do not have the money to waste will take the time to either diagnose the car or pay to have it diagnosed.
Keep in mind the close to 200 dollar fuel pump assembly added to the clutch components and tools you will need to do that job will exceed what you paid for the car.
This means more than ever you need to diagnose the problem, and you need to check the rest of the car over for other issues the new to you car may have.
If you take the time to diagnose your car and look over the car front to rear top to bottom. you will have the information you need to make a decision if you want to keep the car.
Personally I do not think you alone burnt up the clutch.
I think your new to driving a clutch so you probably helped age it some. I am guessing the clutch master and slave cylinder has plenty of miles on it and was ready to go anyways.
to answer your question if you just want to hang parts on the car and replace the pump if it needs it or not.
To siphon the fuel from the tank I am guessing you used a cut garden hose.
This hose may be too large to fit down inside the tank.
Many Automotive parts places have a rattle siphon that is thinner than a garden hose and works on most cars.
here is a link so you can see what i am talking about.
http://www.amazon.com/gp/product/B0...on&qid=1458084479&ref_=sr_1_sc_1&sr=8-1-spell
If you sign up to AutoZone's website for free you will get access to free diagnostic information and repair procedures. It will even give you step by step procedures on how to change the fuel pump if you find you need it.
Once you sign up and you need help finding the diagnostic information let us know and we can guide you where to look.
This is just a sample of some of the information you will find there for free to help aid you in properly diagnosing your car.
Bottom Feed Port Fuel Injectors
Print
TESTING
The easiest way to test the operation of the fuel injectors is to listen for a clicking sound coming from the injectors while the engine is running. This is accomplished using a mechanic's stethoscope, or a long screwdriver. Place the end of the stethoscope or the screwdriver (tip end, not handle) onto the body of the injector. Place the ear pieces of the stethoscope in your ears, or if using a screwdriver, place your ear on top of the handle. An audible clicking noise should be heard; this is the solenoid operating. If the injector makes this noise, the injector driver circuit and computer are operating as designed. Continue testing all the injectors this way.
CAUTION
Be extremely careful while working on an operating engine, make sure you have no dangling jewelry, extremely loose clothes, power tool cords or other items that might get caught in a moving part of the engine.
All Injectors Clicking
If all the injectors are clicking, but you have determined that the fuel system is the cause of your driveability problem, continue diagnostics. Make sure that you have checked fuel pump pressure as outlined earlier in this section. An easy way to determine a weak or unproductive cylinder is a cylinder drop test. This is accomplished by removing one spark plug wire at a time, and seeing which cylinder causes the least difference in the idle. The one that causes the least change is the weak cylinder.
If the injectors were all clicking and the ignition system is functioning properly, remove the injector of the suspect cylinder and bench test it. This is accomplished by checking for a spray pattern from the injector itself. Install a fuel supply line to the injector (or rail if the injector is left attached to the rail) and momentarily apply 12 volts DC and a ground to the injector itself; a visible fuel spray should appear. If no spray is achieved, replace the injector and check the running condition of the engine.
One or More Injectors Are Not Clicking
See Figures 1, 2, 3 and 4
Click image to see an enlarged view
Fig. Fig. 1: Unplug the fuel injector connector
Click image to see an enlarged view
Fig. Fig. 2: Plug the correct noid light directly into the injector harness connector
Click image to see an enlarged view
Fig. Fig. 3: If the correct noid light flashes while the engine is running, the injector driver circuit inside the PCM is working
Click image to see an enlarged view
Fig. Fig. 4: Probe the two terminals of a fuel injector to check it's resistance
If one or more injectors are found to be not operating, testing the injector driver circuit and computer can be accomplished using a noid light. First, with the engine not running and the ignition key in the OFF position, remove the connector from the injector you plan to test, then plug the noid light tool into the injector connector. Start the engine and the noid light should flash, signaling that the injector driver circuit is working. If the noid light flashes, but the injector does not click when plugged in, test the injector's resistance. resistance should be between 11-18 ohms.
If the noid light does not flash, the injector driver circuit is faulty. Disconnect the negative battery cable. Unplug the noid light from the injector connector and also unplug the PCM. Check the harness between the appropriate pins on the harness side of the PCM connector and the injector connector. Resistance should be less than 5.0 ohms; if not, repair the circuit. If resistance is within specifications, the injector driver inside the PCM is faulty and replacement of the PCM will be necessary.