I am travelling with Lufthansa Rail and Fly. Taking train from Dusseldorf to Frankfurt and then plane from Frankfurt to Baku. I have only 1hour, 12 mins layover in Frankfurt. Is it reasonable time to get to my flight on time? Do I have to register my baggage or pass throught security control again? Thanks.
Short answer: NO if you do indeed have a Rail and Fly ticket. OK if you confused it with Express Rail (I think this was previously called AIRail). If you are unsure, check this excellent answer to figure out what applies to your situation.
Hilmar and rugdealer answers seem to answer the Express Rail case: You check in at Düsseldorf train station and get a boarding pass even for the train ride. Lufthansa tells you that it's doable, and they will take responsibility if anything goes wrong.
However, your question says Rail and Fly, and if that is what you have, then I would strongly advise you to take an earlier train. As mentioned in the other answer already, Rail and Fly allows you to get a free/cheap train ticket to get to the airport on you travel day (or the day before). However, arriving at the airport on time is your responsibility and yours alone. On this website, Lufthansa clearly states that you have to search for a good train yourself:
The travel times for your train journey shown on your itinerary do not represent valid connections. To find the best train connection for your journey, go to www.bahn.de
If the train is late, Lufthansa will most probably NOT rebook you for free.
There is no difference between both options when it comes to dropping your bag - there is a bag drop right next to the train station that all Lufthansa passengers can use - or going through security / passport control. FRA is huge and lines can be long... if you plan to arrive only 72 minutes before takeoff, better be prepared to run.
It's tight but doable. You can drop your bags the AirRail terminal right at the train station in Frankfurt airport https://www.frankfurt-airport.com/en/flights---more/transfer.detail.suffix.html/article/flights-and-more/at-the-airport/AiRailCheck-in.html
You still have to go through security and hike to the gate (which takes a while since the airport is very large). If baggage line and security line are "normal" you should be okay. Yesterday, however, I spent about 30 minutes just in the security line. Unusual, but it can happen.
If it's all booked with Lufthansa as a single trip, you should be reasonably safe. If you miss your connection with and it's nor your fault, than they will rebook you on the next flight for free.