When your car is hesitating (engine almost die) while you want to accelerate and under the hood (bonnet) everything is fine (like ignition system, timing belt, lambda sensor, TDC crank sensor, you have fresh oil, etc.), it's time to look closer on fuel system (replace external fuel filter, and if it's still no good, fuel pump may be guilty - you can measure the pressure and/or inspect the pump and tank, to check what's inside, pump inlet clogged or something like that).

In my case it was easy, because fuel pump one day started to squeak/whine.

There are fuel pumps as a separate device or "complete assembly" kits available.
00-YouCanBuyPumpItself.jpg

I decided to buy whole assembly kit.
01-NewPump.jpg

Punto 1,1 SPI (it's 1 bar pressure pump, for more powerful engines pumps are 3 bar).
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In this type of kit, you must install level indicator, floater, correct way.
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Important thing. With new pump, you need new inlet filter - it comes with "complete assembly" kit. If you are buying separate pump, there is chance, that they will not give you this. That's why it's better to buy complete kit.
02-NewPumpFilter.jpg

Fuel pump is located under the back seat. Just pull it up, to expose fuel pump cover.
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Remove (with screwdriver) this metal cover, and you will see the fuel pump.
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Release tank pressure (vacuum), leave it open during replacement procedure.
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Fuel pump is tight on position because of big plastic nut holding it. Spray a lot of some penetrating oil and wait a while.
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Start the engine, let it idle for a moment, and pull out the electric plug/connector on the pump. Engine will die, and there will be no pressure in fuel lines. Now you can gently remove fuel lines (remember where is IN and OUT).
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I have heard the horror stories about enormous problems with undoing plastic nut. Mine was easy to unscrew. I just tapped it with punch/chisel and it started to move.
If you have problem, try to use two chisels and hammers at the same time. If it fails, you will be forced do make, improvise your own SST (special service tool).
This (removing big plastic nut) is the one thing that can really go wrong - generally difficulty level of this job is 1 (one).
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Nut removed...
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Old fuel pump assembly removed. Be careful with this black rubber gasket. Clean it, keep it. During installation of new pump, gasket goes first into tank hole, then goes the pump.
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Now you can look into the tank. The is some dirt (dust, sand)...
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It is recommended to have low level of fuel during this procedure - it's easy to clean tank.
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You can find strange things inside - this is piece of wood...
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Mind the gasket mentioned somewhere above. Put it first, then gently place the new pump assembly into tank (be careful with level floater, don't break it or bend it).
Tight the plastic nut (you can lube it with the same penetrating oil used to removing it, or silicone grease/oil) by two hands only (no tools, no hammer punching).
Tight until pump assembly will stop moving, playing freely under the nut. It's enough to keep it in place and make it sealed. Put back fuel lines (mind IN/OUT), hoses. Connect electric plug and it's done, ready to test drive. Then fasten metal cover, put rear seat on it's place, and that's all. There is no need to make air-bleeding.
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Why there was hesitation (not enough fuel)? Because internal filter was clogged...
23-OldPumpFilterClogged.jpg
One more important thing - never run on low fuel level ("E", "reserve"), especially in winter (when it's freezing), because water condensation inside tank can freeze and damage the pump (mine started to make whining sounds about 2-3 weeks ago, when temperatures were negative, about minus 10°C in place where I live).
In the other hand, when it's really hot, pump needs to be cooled down - fuel acts like lubricant and coolant to fuel pump.

If you want to replace pump itself (not entire assembly), go ahead, but remember about filter also (inlet filter from this picture, in-line fuel filter outside tank is a different story).
25-OldAssemblyDismantled.jpg

That's all. Little bit messy, but simple job.
If something isn't clear - sorry, English is not my native language.