Correct on segmenta. More to the point, segmentum Administratum cannot realistically do more than set vague policy for the vast dominions under its control.
Segmentum Command for Guard and Navy units fulfils a more practical function - providing logistics and Lord Generals, Lord Admirals and Warmasters for the really, really big wars.
Most matters are resolved at a lower level, however.
Sectors - and subsectors - are not universal. That is, not every world is part of a sector. Sectors exist where sufficient worlds are close enough together and accessible from one another to be worth having a mutual organisation. Imperial worlds outside sectors are rare (because they tend to get destroyed, being comparitively easy targets) but do exist.
Where there is a sector, there is always a lord governor sector. In theory you are correct that this is an administratum rank, but the man holding it is not always a member of the administratum (sometimes he is nobility, sometimes ecclesiarchy, sometimes - e.g. ultramar - he's not even technically human). The appointment is recognised by the administratum but is not made by it; if there is no trouble and tithes met, the administratum does not interfere with planetary government, so you can elect whoever you like, however you like - democracy, hereditary or dead men's shiny boots; the administratum doesn't really care.
You are correct that this is very fuedal - the lord-governor sector has no 'superior' accessible or consultable within months of warp travel and weeks of astropathic delay, so he essentially has carte blanche to protect his domain. It is literally planetary governor writ large, amalathian oath and all.
The limits to a lord sector's authority largely come in the form of those subordinates (there are some) over whom he has advisory but not direct authority - the guard and navy chains of command feed back to segmentum command, so in theory he can't give them direct orders. He can, however, give PDF and SDF forces - of which a sector has a LOT - orders, but they're less capable and restricted to their home systems. Astartes forces and the Holy Ordos are also not answerable to him, ditto anyone serving the Mechanicum or Ecclesiarchy.
There are also Lord Governor Subsectors - indeed one is a major character in the Ravenor series by Dan Abnett. Their level of power is not fixed by imperial law in the same way, and will vary from sector to sector - the more inaccessible the subsector, the more independence the Lord Sub will need, and the weaker the Lord Sector, the more authority will pass into the hands of his subordinates. By comparison, not all sectors even have them; Calixis has some subsectors with subsector capitals (the most prosperous ones) and ruling authorities, but not all calixian subsectors do. Equally, at least one subsector's 'subsector capital' will invariably be the sector capital (scintilla in the case of calixis) where the lord sector can enact his will in precise detail without delay or interpretation, so no subordinate governor is needed.
There isn't really a system/planet level. It's extremely rare for multiple 'primary' worlds to exist in one system - the planetary governor generally assumes responsibility for off-world mining outposts, lesser colonies, etc, etc. See quite a few Ciaphas Cain books for examples.