Why stop the rotation at 5 degrees? On all the Boeings I know the procedure is to rotate straight to ~15 degrees. At that point you hold airspeed V2 to V2 +10 until you start the flap retraction. And there is a difference between pitch attitude and angle of attack. Most airliners don't show AoA so there is no way to reference it.
You don't normally climb in vertical speed mode, that has killed people. You have a target climb speed and climb thrust. Your rate of climb is whatever it is.
1. On a 747-400 you start 4 and 1 then 2 and 3 when 4 and 1 are stabilized. On a -8 wait 10 seconds after starting 4 before starting 1 and 10 seconds after starting 2 before starting 3.
2. Descents are the same as climbs, reduce the thrust and hold a target speed. That being said, unless ATC has assigned a hard speed, if you need to get down quicker increase the airspeed.
3. Single engine taxiing is normally a weight issue. Some airports forbid it.
4. Again, set climb thrust and hold your airspeed. Your rate of climb will be what it is.
5. Most airports that transport jets operate to have STARs and SIDs. All the FAA ones are available free online. How relatively real do you want your sim to be?