I am fairly certain the 1870 census in Rosendale showing Frederick Lutze (probably really screwed up by the census taker) is the right guy with family. Plus this fits with other info and helps to answer lots of your questions. Another reason I think this Frederick in 1870 is your John Lietz is because in the 1910 census, John is listed as John F. Lietz.
In my experience in German records, normally they have 2 or 3 first names, and the GTA listing shows Joh. which normally is short for Johann. So I think his full German name would be Johann Friedrich Leitz, or Americanized to John Frederick Lietz.
This 1870 census also shows 2 kids, Bertha and Emma, and both born in Wisconsin, probably Rosendale. The 1880 census is most likely in error, showing the first 5 kids born in Prussia, and they should all be born in Rosendale, Wisconsin or nearby.
This makes sense when you look at the other info in the other census showing marriage in 1865 and the first born Emma or Bertha born in 1866 in Wisconsin. Also John Lietz, b. Oct 1869 shows born in Wisconsin in the 1900, 1910, and 1920 censuses, which proves more of the error of the 1880 census showing John born in Prussia.
So my best guess is John Leitz met and married his wife, Henrietta in 1865, or shortly after John arrived in 1865 in Rosendale. John then purchased land in 1866 according to your records.
The 1900 census shows immigration in 1865, the 1910 census shows imm. in 1864 (hard to read) and Hattie in 1859, and the 1920 shows imm in 1870. The census is usually in error with these immigration dates, but the 1865 matches with the one Joh. Leitz I have in the GTA, arriving in 10 July 1865 on the ship Saxonia. The 1920 census shows naturalized in 1875 so this looks appropriate because it takes about 10 years.
On the microfilm, which one did you order?
The one I would order is the Hamburg Passenger Arrival, direct list, film number 0472896, Bd. 19 for 1865; or the name index, film 0884672 for names KATZ, Samuel to LEWIN, And.
Usually they are on the direct listing, however if he is not on the direct listings then try the indirect list.
These films numbers are from:http://www.genealogienetz.de/misc/emig/ham_pass.html#dirlist
The Arrival Passenger list at NY usually does not have any info on the town in Germany, and this is where the Germans To America series gets its info. However the Hamburg Passenger Departure Listings normally show the town in Germany. From this you can order the parish that serves the town. The parish can normally be found fairly easily through the online info at the Morman site in the Family History Catalog, or at this German site under Locations:http://www.mfpev.de/
Looks like your in for some fun and excitting research!