Best approach for reverse engineering an RF Remote for a newbie
You can use RTL-SDR dongle and either put together a decoding package using gnuradio or see if anyone did this already for your remote. Protocols for many remotes, utility meters, weather stations, etc. have been reversed already.

To replay the data you'll need a transmitter. There are ham radios for your band but chances of finding ready-made software for your protocol are low. Again, gnuradio can be used for that.