A little bit of logic, a little bit of technique and everything works out ...
1)
slope: it is inscribed on the elbows "at 90 °"
-pvc pipes = bends at 87 ° 30 = slope 2.5% / m
- PE / PP pipes = bends at 88 ° 30 = slope at 1.5% / m
2)
ventilation: (well explained dedeleco)
-pvc pipes: compulsory primary and secondary ventilation, either by venting (beware, it is the direct sewer, it stinks, not very close to a window!) or with an 80mm aerator (a small 50mm is not enough).
- pe / pp pipes: primary ventilation compulsory, secondary ventilation unnecessary because 90mm wc outlet and 110mm horizontal pipe ==> is never filled (no piston effect). See the principle on Geberit evacuation.
http://www.geberit.be/web/appl/be/wcmsbef.nsf/files/usr-pdf-%C3%A9vacuation_FR_low.pdf/$file/%C3%A9vacuation_FR_low.pdf
or on unipipe
http://www.pipelife.com/media/be/PipeLife_Catalogus_2010.pdf
(on page 11/187, there are cast iron / pvc or pp fittings)
3)
the corking:
diameter of a toilet (pipe): 90mm / 110mm. too small it clogs, too large (ex 140mm) it's badly rinsed and it clogs too!
hunting principle:
-3L = undocumented
-6L = with papers
A T with cap for possible unclogging is not superfluous ...
Petit HS: well no, 6m is not very long, how many villas are connected to the public sewer (street) and set back 15 / 20m or more? And horizontally, and 140 / 160mm? and with a slope of 1%? And it does not get blocked ??? Well no, because each storm / heavy rain comes to rinse everything properly ...
4)
the cast iron / plastic connection:
THE tricky point!
Many solutions:
-If cast iron pipe = 100mm inside, work with 90mm pvc, fit it vertically 20cm then silicone sealant (or putty) for odors.
-If it is 100mm outside, you must start from a collar. Good luck with the disassembly, they were often connected with molten lead for sealing.
-Below your cast iron (underground) you certainly have a sandstone pipe (normally 110mm)? If you can go find it, would it be simpler?
-To not disassemble the cast iron on the height, you can either:
-see if you can get the unipipe fitting

or if a pvc / stoneware "sewer" connection could be used.
-use a Nicoll straight toilet outlet
http://www.nicoll.be/fr_BE/catalogue/specialites-sanitaires/accessoires-wc-pvc.html
In short, a lot of things are possible, it's up to you to decide according to your technical skills / the equipment available / what is in place.
Good research!
Sometimes it is better to stop, reflect, and ask the right questions ...