Do dogs generally change after being fixed?

Essentially no, they will still have their personality. Just when they get older they wont develop anxious or nervous behavior due to a need to mate all the time. Once the drugs wore off, my dog recovered fairly quickly after being spayed. After a week she was all better and the wound was almost completely healed. Just don't let them lick at the wound, and try to limit activities to low impact (ie walking, not running) for the next week. Another thing you might want to look into is the amount of food your dog should be eating now. I know for some female dogs can start to gain weight after being spayed, due to the body not pumping all those hormones. You might want to consider giving them a little less food than you did before.

They shouldn't change drastically. Their basic personality shouldn't change. But it will significantly help with many behavioral problems. Spaying/neutering a dog can help potty training, aggression, basic obedience, hyperactivity, reduces stress (on both dog and person), anxiety, etcetera. When you bring them home from the vet give them somewhere that is out of the way and quiet so they can sleep off the drugs. Other than that just try to keep them calm and clean and refrain them from jumping too much so they don't rip their stitches. And just keep an eye on the stitches to make sure they stay intact and don't get infected.

Depends on when they get fixed. Their base personality wont change, but their aggression (or ability to attract aggression) and energy levels may change to one degree or another - every dog is different.

Keep your dog comfortable, first day they might be anxious since they would be uncomfortable. They should have quiet isolated place to stay for the first couple days. Within a day or two their appetite will return. Keep walking or any activity down, especially with external stitches. Keep the incision site dry and clean, and try to keep your dogs mouth from reaching it, and immediately report any changes to the vet.
Most importantly listen to the vet says and follow their directions.

Yes they do since hormone are no longer present once the testicles/female organs are not there .

Yes, they do since vital hormones are no longer there. For the second part of your question, follow your vet's advice.

Yes they can do, just as stallions and geldings are different, and one is more suitable for a beginner than the other because it is calmer and more tractable, so castrated and entire male dogs are different.
With b!tches its a different matter. Spaying can make dominant b!tches more dominant.

Its not a cure for behaviour problems. All it does is remove the ability to procreate. They'll still hump and fight.

After surgery keep them quiet for at least a week, especially females after spaying. Dont let them jump up on furniture or run up and down stairs. Keep them on the lead when you take them outside to pee.
Its essential they drink and pee within 24 hours after surgery to flush the anesthetic out of their kidneys. You can offer 50/50 warm milk and water, as the risk of not drinking is higher than a mild upset stomach.

Their personalities are shaped by their genetic breeding and their experiences with socialization and learning. It is not tied to their nuts or womb.

Males heal in 2 days.

Females have the abdominal surgery and need to be on pain killers for a few days, with no active running for maybe 4 days.