Good questions. In regards to if things are as bad as some rumors say it depends on which rumors you have heard.
Parrots can be wonderful pets however they are not for everyone. Auggie has added more to my life than I could ever express but there have been many times where he's been very aggravating.
Do they bite: How much/often they bite depends on many factors of how you raise them and care for them. Note though that ALL parrots will bite at some point or another - and it will hurt. I have a couple scars on my hands; if this absolutely unacceptable then a parrot is the wrong choice. However the way you phrased the question indicates that you know SOME biting may be inevitable. I suspect the rumors you heard may be overstated.
Are they hard to train: as a behaviorist I have often found it is the owners who are much harder to train than any animal. With the right knowledge, techniques, and patience they can be trained well. But parrots in general do take more work than other common pets.
Sex differences: virtually non-existent in my opinion (which here I will admit I don't have species specific experience). Females of course have the risk of reproductive issues such as egg-binding. Behaviorally however individual characteristics outweigh sex characteristics.
Loud: YES. All parrots can be quite loud. As much as I learned before getting my conure this was one thing I was not prepared for. As for the constant part this largely depends on how they are kept. For the most part it will not be constant if you give appropriate out-of-cage time, toys, and entertainment. Most parrots have one or two scream-times per day. Vocal behavior is a normal and healthy thing for parrots and screaming is part of this; you can however work this into a nice schedule.
Mess: YES, another thing I was not prepared for. A dust-buster/hand-vac will be your new best friend - or hopefully second best if the bird is your best. Parrots can be potty trained to go in a certain area, but until then "accidents" will be common, for a while Auggie would go on my shirt, especially clean ones... Now Auggie has relatively rare 'potty-accidents' but they also tend to throw food around a bit so the area around his cage is in regular disarray.
I may make owning a parrot sound miserable and that is not my intent. Despite these concerns bringing Auggie home is one of the best things I have ever done. It is not a decision to take lightly however. A well raised parrot will not bite OFTEN, will not scream CONTINUOUSLY, and will not make a HUGE mess. A parrot can be the right choice for you if you are ok with some biting, some screaming, and some mess - regardless of training and care these are part of parrot parenting.
