Many powerlifters are doing maxes very frequently, but for the average to slightly above average lifter doing it 2-3 times a year is probably sufficient.
You want a lot of your work to be percentage based, but you do need to go for a true 1RM at least once a year to make sure your numbers are right.
For me, estimated 1RMs are directionally good but I haven't found them to be terribly accurate. There is just something different when doing squats with 315 for 10 reps (430lbs estimated 1RM) and then throwing 405lbs on your back.
When you ask a novice powerlifter about recovery, they will often tell it takes a good two weeks to get back into the gym after a pretty serious competition. It isn't so much physical as it is mental.