Manuscript hasn't been sent to peer-review for two months
There is no general answer to this kind of question. It is field or discipline specific. For Computer Science (or, mainly engineering disciplines), it is very normal. The following would be my interpretation:


  The status of my manuscript has been "editor invited" for one month ...


Let me guess that the manuscript was submitted in May. Probably, for some time, the journal admin (or assistant) was on leave. So, (s)he sent the invitation late and the process got delayed. Moreover, the intended editor was on leave as well to support the delay.


  .. and now a month later, it's still "editor assigned". 


It is good that the invited editor has accepted the request to handle the manuscript. And, probably (s)he is searching for reviewers; or, already has sent the review requests to many researchers, but none has answered yet because of the summer leave.


  Should I inquire about the status of the manuscript? The journal stated that it takes 4 months from submission to first decision, but I am unsure what first decision is, and whether it includes desk rejections or not.


I don't focus on these statistics. These hide relevant details. These statistics are usually skewed to two ends 'desk rejection -- 15 days', and 'first peer-review comments received -- 10 months'. It is actually an 'unreliable' mean estimate.