Okay... I've rang UKVI (
https://www.gov.uk/contact-ukvi/european-nationals)
Here is what they said:
In our situation the whole application is based on the EEA national, and the non-EEA spouse only needs to fill in the section 5 to be included on the application as a family member.
No need for section 2, and no need for section 11 altogether.
I have also asked about questions 1.3 and 1.4 (name and surname), and was told that in this case full name field 1.3 requires the first name (and any middle names) only, and the surname goes separately to 1.4.
The adviser told me that I don't even need to fill in the section 5 myself because all my absences from the UK will be on my wife's section 5 as I am her sponsor.
I wrote down the answers, and went through the forms once again. Many places didn't seem very logical, so I decided to give UKVI another ring. It turned out I was extremely lucky the first time I rang because none of them would agree to discuss forms with me anymore, saying that I need to hire an independent immigration adviser for that purpose.
Would anyone be able to confirm the information above? Perhaps ring UKVI once again and try to get the information?
Anyway, I guess that the key is question 3.1 on page 23 which instructs an EEA national to complete sections 5, 9, 16, 17, 18 and 19.
Based on the text
"(If you are or have been a family member or extended family member, also complete the relevant section(s) as indicated in question 3.2 below.)" there is no need for an EEA national to look at question 3.2 (if they are not, and have not been a family member of an EEA national).
That's a contradiction of course... which can be resolved by a clear definition of a term "family member". Logically, if I am an EEA national, and I have a family, then I AM a "member of a family of an EEA national" (my own family), but if there are no other EEA nationals in my family, then I can't be called a "family member of an EEA national". Again, even if my wife is not an EEA national, I can still be a family member (or extended family member) of an EEA national, for example if my parents are EEA nationals.