How can I apply italic fonts for labels and print composer in QGIS 3.4?
The option seems to be disabled.
To apply italic fonts for labels there are two ways to achieve this and depends on the type of label you are adding.
When you load in a dataset into QGIS, you can then go to the properties - labels tab and select if you would like to have label and from which field. There you can modify your font to italic. Once you create a new composer all your properties from the QGIS canvas will carry over. You will not be able to modify the label of a dataset once in composer.
Also, if you were to add any labels once in composer you will than be able to modify the font in the label tab once you select the label item.
In fact it depend on the font you use, for exemple on my setup Arial font let me choose 6 different style (normal, bold, italic, narrow, black and black italic) other font may have only the normal option or offer more than 10 different style depending on how they where created.
The way to access these option is by the style menu, not by clicking the "I" button that seem to be always disabled (I think you only use it for data defined override) .