Is the null in the direction better if the antenna is bigger?

Not necessarily.
Null and sensitivity are generally better in larger loops, but the nulls are principally determined by the capacitive balance of the loop.

Is the directionality influenced by the distance between windings?

Not necessarily.
A lot has to do with the physical construction. The term "balanced" (physically and electronically) has some meaning here.

Will the sensitivity be improved by taking more windings or a larger frame? (Capacitor should of course be reduced to keep LC product in the right range.)

Yes, either will improve sensitivity. The output voltage is directly proportional to the loop area and the number of turns.

Is it true that the low directionality for some stations is due to electrical pickup?

Yes; imbalances in the loop (principally capacitive coupling) cause the entire loop structure to act as a short vertical antenna which is added to the loop output. This is often called "antenna effect".

Re-radiation from electrical wires, appliances, etc. can also cause "skewing" of receiving patterns and nulls. In such cases, the expected signal may be best, or the QRM nulled best, at unexpected directions. I've found the best place to use a loop antenna is in a middle of a field where it's sometimes just as easy to erect a Beverage antenna...

Where does the antenna take most of this pickup: in the primary coil (28m wire), the secondary coil (8m), or the feed line (2m of twin-lead chord (perhaps coax would be better?)?

If the loop is well-balanced (principally symmetrical capactance to ground from all parts of the loop, including the pickup and feedline), then most of the pickup should come from the tuned main loop (28m wire).

Instead of the 2m twin-lead chord you should feed the signal to the receiver with coaxial cable. Otherwise this is very possibly a secondary pickup point of signals (especially local ones), giving you inconsistent sensitivity and null.

How can electrical pickup be reduced? I tried grounding the primary coil but this kills the signal. Grounding the radio or the secondary coil has almost no effect on interference or directionality.

´ No mystery there. Shunting the signal to ground will kill it. The ability to tilt the loop (from side to side) is also important to attain deep nulls and to reduce local noise. Antenna phasing units can sometimes also be used to cancel noise. I have used my own phasing unit for this purpose. Several such products are available commercially, one of them from from JPS another from S.E.M.

May 22, 1995 in Usenet's rec.radio.shortwave Gerard Tel (gerard@cs.ruu.nl) asked. Steve Byan (steve@hi.com) answered.

For more information, you should consider getting the NRC booklet on loop antennas:
"Loop Antenna Design and Theory"
NRC Publications Center
P. O. Box 164
Mannsville, NY 13661-0164
USA
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