Yes, a floppy drive has at least one stepper motor that will produce current peaks while making steps.
Check with an ESR-meter that any electrolytic filtering capacitors are still in good shape (and not dried out). Electrolytics on the supply lines act as small local energy tanks that will supply the extra current bursts needed by whatever circuit is nearby the electrolytics. If they have lower than nominal capacity, or if they have high ESR (Equivalent Series Resistance), they won't be able to supply peak currents, so all the other circuits will see a drop in voltage at each current peak. This can make a computer crash.
1. - make sure you have thick wires to the power supply
2. - wires must be copper, not the chinese iron wires (often terminated with alligator clips), iron wires are not good, you can detect them with a strong magnet, if your power supply wires are magnetic, replace them with thick copper wires.
3. - not nice to ask only, without reading/answering the questions