You can buy a cheap multimeter at Harbor Freight or Home Depot.
You should learn the basics of electric circuits if you want to proceed diagnosing electric circuits in your car - don't want to be mean, just stating a fact.

I don't know which pins are which, but you can check that in ETM which is a part of service manual of your car. High speed operation bypasses the pre-resistor, that's why it's high-speed.
From what you've written, it means the relays are getting power. It also means wiring from fusebox to fan is good.
I'm not sure but your relays may be bad. I'd replace your relays with a set of newer ones from junkyard, it should cost a few dollars.
If pre-resistor is intact visually, it's usually good.