Is it possible to connect diodes in series to increase reverse voltage capability? Is it possible to connect them in parallel to increase the forward current?
Yes. Diodes can be connected in series and/or parallel in order to increase the reverse voltage and/or forward current capacities.
There are practical considerations to keep in mind such as thermal management, voltage isolation, and component count, to name a few.
When connecting diodes in parallel it is usually a good idea to match Vf. Differences in Vf between diodes will get worse as they heat up. Diodes with lower Vf will initially conduct more current, increasing their power dissipation and further lowering their Vf. This in turn increases their current share, continuing to heat up the junction, and so on until a catastrophic failure occurs.