Values in the Pivot View are result of aggregation, so you should not try to edit those results. You should make amendments to the data while still in the Table View, or rather in the Data Manager, using the Search/Replace operation block.
Does it mean that within data manager I have to duplicate each field and add a formula "If = "", "0", ". That's the only way I can enter "0" which is not much of use.
Syntax is IF([Field]=null, not IF([Field]=" " or IF([Field]=0. Blanks are nulls NOT zeros. You may wish to provide more detail, so we can look into this - you attached a screenshot, but provided little in terms of explanation. What is 'previous version of pivot table'? How did Omniscope arrive at (no value)? If it's adding up empty fields, then result should be (no value) rather than zero. If you prefer to see 0, then you should populate empty fields with zeros, using the Search/Replace operation, in Data Manager, rather than IF function in Omniscope. Video tutorial is here: http://tc.visokio.com/videos/?name=DataManagerSearchReplace&title=Search%2Freplace&lang=gb
Dariusz, please note, the (no value) in the 2.8 Pivot view is actually a bug we'll be fixing shortly. Cells without any values (not even zero) should appear blank.