1. If the time period is not critical, relays would work but time could be +- 5mS.
2. Back EMF suppression will be a problem what ever form of control you use, relays are more forgiving the transistors, and if plug in are easier to change. Just remembered, switching DC with relays puts extra strain on their contacts as the arc is not self extinguishing. Relays that are rated at 2A @230V AC are rated at 12/24 V DC, so finding a sufficiently rugged relay, for a long life could be a problem.
3. A couple of NE555 timers would do the job for the timing and both time periods could be adjusted for optimum performance and some form of interface to power the main relay (s)
The system has to be fully specified, i.e. when you apply power what happens, when you switch the motor on what happens, which direction it runs in, emergency stop, etc.
Frank