Top half of the aggetater isnt conected to anything..it just spins around by hand..is this normal?

The pump impeller will not spin as you think it should, the impeller is connected to the rotor of the pump motor which has magnets fitted.
When turning the impeller by hand this will only give you one half revolution as the magnetic field stops the impeller from spinning around.
This is perfectly normal.

You most likely are not hearing water remaining in the tub. You are hearing the water slosh around in the balance ring that is attached to the spin basket. There is a balance ring attached to the spin basket that is half filled with water. When the basket is turned by hand you will hear the water in the balance ring. This is normal.

You mentioned pet hair. Remove the brush cover and check for a plug (possibly pet hair). Sounds as though you have a plug somewhere and it's not allow the suction to pull it through. Also check your filter and clean or replace as necessary. Hint; Never let you container get over half full, it reduces the suction.

Whirlpool, Roper, an Kenmore are the only brands with rebuild able agitators. Any other brand will need a replacement agitator. The parts are about 6 to 8 dollars.
Here are some instructions I recently posted for someone else with a similar problem on an older whirlpool washer. If you need more specific instructions or the model you have is different let me know and I can look up the parts breakdown and give you step by step repair instructions.
Does the lower half of the agitator still operate normally? (Back and forth) Can you spin the top half (spiraled part) of the agitator in both directions with out the lower half moving? If so then you have a worn set of agitator "dogs" they are little plastic ears located in the upper half of the agitator and catch the notched inner section of the agitator to make the top action work like a corkscrew, slipping one way and driving the other as the lower half goes back and forth.
To get at these parts you will need to remove the agitator, Remove fabric softener dispenser or cap on top, and look down inside tho opening.
You will need to remove the plastic cover inside that has two ears sticking up, pull on one side or the other and it should pop out, there will be a rubber seal around it so it will be a little difficult to remove.
Now you will have access to the bolt that holds the entire agitator in the machine. The agitator dogs are located right on the outer edge of the center cup that the bolt goes through. To access them you will want to separate the two halves of the agitator and flip the top half upside down while holding your hand inside it to catch the cup with the dogs in it. Part number 80040, for the dogs.
Good luck to You!!

Does the lower half of the agitator still operate normally? (Back and forth) Can you spin the top half (spiraled part) of the agitator in both directions with out the lower half moving? If so then you have a worn set of agitator "dogs" they are little plastic ears located in the upper half of the agitator and catch the notched inner section of the agitator to make the top action work like a corkscrew, slipping one way and driving the other as the lower half goes back and forth.
To get at these parts you will need to remove the agitator, Remove fabric softener dispenser or cap on top, and look down inside tho opening.
You will need to remove the plastic cover inside that has two ears sticking up, pull on one side or the other and it should pop out, there will be a rubber seal around it so it will be a little difficult to remove.
Now you will have access to the bolt that holds the entire agitator in the machine. The agitator dogs are located right on the outer edge of the center cup that the bolt goes through. To access them you will want to seperate the two halves of the agitator and flip the top half upside down while holding your hand inside it to catch the cup with the dogs in it. Part number 80040, for the dogs.
Good luck to You!!

It is normal to have residual water in the drain lines and pump following a wash cycle. This is the low point of the drain cycle and gravity will ALWAYS cause some water to be there. As long as the water is not visible in the spin basket, you have nothing to worry about.

Some model washers also have a balance ring around the perimeter on top of the wash tub that is filled with fluid. This acts as a stabilizer to help keep the washer balanced during the spin cycle. If you have any questions, please post back and let me know. I hope this is helpful to you.

You could have something inside the dryer dragging on the dryer drum. You can unplug the dryer and lift the top *(your dryer lid is held on by spring clips just push up on the front edge and it should pop open, tilting up and back) Look around for anything in the area of the drum that doesnt belong there...a sock...a pair of shorts...dryer lint...you get the idea.

If you dont see anything you may have a drum roller going bad. That will take a bit of dexterity to check out but you should be able to see if one of the roller looks like it isnt turning. Give the drum a turn by hand and see if a roller is hung up.

Good luck and be careful.

Take off top and rear half of machine cover
remove belt and spin drum by hand, (does it spin freely?)
make sure pump and drain hose are ok (clear)
there is a plastic ball (about egg size) in hose from drum to pump.
check motor brushes are at least 3cm long
if you have checked all these but the fault persists email me on [email protected]

with the machine off, turn the cycle dial around 3x very harshly, then try it again. If it works normally now, you'll need a new cycle switch soon!

check to see if your pump is slightly plugged with a sock or ?

Your top loader should pump out in about a minute and a half when totally full of water.