Problem 3. was solved by Tadeo Baba (privat communication).

Problem 9. : Related paper is listed as No. (with Aurel Cornea). The best source of related informations is the series of articles (approx. 10) by W. Hansen and N. Nadirashvilli. Consult Mathematical Reviews or MathSci (Hansen-W* in au).

Problem 13. (with Ivan Netuka): No progress was registered by the authors.