As much as I know (have it from the Hoffenheim club page) the tickets include the train tickets by regional transfer (trains or busses) in the RNV (Rhein-Neckar-Verkehrsbund). Tickets from Frankfurt to Sinsheim or Heidelberg aren't included - but tickets from e.g. Heidelberg to Sinsheim and back for the match.
Additional trains for the match to and from the Arena into various regions can be seen in the following PDF (starting in Ludwigshafen with stops in Mannheim, Heidelberg etc. ending at the arena - and back)
http://www.s-bahn-rheinneckar.de/s_...erkehre/2018/mdb_279538_181002aushmancity.pdf
No. It should not. If you look for the train (if you do not take one of the above mentioned) look that you only take regional trains that are part of the RNV (Rhein-Neckar-Verkehr GmbH) as they are included into the ticket price.
You cannot really answer that question. There is always a contingent of Spartickets with cheaper prices if you book earlier - but there is restrictions with them as they might not be refundable or changeable. And there is other possibilities like group tickets if you take special tickets or make special tours. If you e.g. go from Frankfurt to the area in regional trains you could take the Hessenticket that costs 35 EUR with 5 persons - if I am not wrong it will get you to Sinsheim like this as the ticket is free in the RNV area that should border to Hessen.