Please give us a model number. Your first issue sounds like the timer is going bad. The second (not spinning all water out) depends on model. You stated its older so I'm going with a direct drive made by whirlpool. If this is so it may be as small needing a coupler to the transmission isn't staying in neutral while draining. Give us more info for further assistance.

Thank you for the fast reply. You do have a whirlpool manufactured direct drive model and I agree this was probably the best designed machine. Let's work on one issue at a time. Since you have a technique in place for rinsing we can explore the slow spin, not draining problem. The issue as I said may be anything, so lets start simple.
1. A stuck piece of clothing between the outer tub and inner basket. Watch Matt from APP show you how to remove the body from the frame of the washer. https://www.youtube.com/watch?v=hfr-m5iXh3s This will give you access to see the inside of the machine, stop the video after he removes the body. With the body removed look at the plastic outer tub and see if you can detect an article of clothing squeezed in between the out and inner tubs. If so remove it by taking off the tub cover see the video starting @ the 4 minute mark. then use a coat hanger to get between the tubs and hook the clothing to pull it out.

If this isn't the problem then:
2. Motor drive coupler may be bad. Watch Matt in this video to check yours. Whirlpool 285753A Whirlpool Direct Drive Washer Motor Coupling - AppliancePartsPros.com the video is embedded with the pics on the left.

While you have the machine apart look for any broken or loose springs at the base as the cause of the leaning issue.

Do these things and get back with us to continue the diagnosis.