Meanwhile the original size of the relevant pictures being different(pictures stored in Gedcom file), is it possible to adjust automatically the same size for all of them in the family tree?
Unfortunately, that is not possible. You need to either use pictures that are all the same size or manually adjust the icon sizes after setting the label icons.
For an unknown reason, after solving the subject of pictures I got a trouble: all the texts (corresponding to persons' names) of the nodes are not any more displayed.
What is the solution to recover these names?
That depends on why the label texts are no longer displayed.
If you are mapping your pictures to the icon of the first label, maybe setting the icon of another label already helps. (With a default GEDCOM import, each node will usually have up to three labels - one for the name, one for the birth date, and one for the death date. Thus, you could try setting the icon for the fourth label. See the "Map To Label No" field in the properties mapper configuration.)
If you are already setting the icon of a higher-index label, maybe that label simply overlaps your text labels. In this case, you would need to adjust the label placement.