Pur_SSyn, I will keep my answers slightly less technical, so they are more rules of thumb than the absolute truth.
1. What is the maximum landing speed of either plane in Knots, or MPH?
Most of the aircraft you named will have normal landing speeds of between 130 to 150 kts. In abnormal conditions (flap problems or other abnormal configuration), this speed will increase, but as mentioned will be below the tire limiting speed of usually around 180kts.
2. What is the maximum approach speed of either plane in Knots, or MPH?
Most aircraft will attain very close to their touchdown speed quite early on final approach, because most airlines have a "slot" between 500 - 1500 feet above ground where you have to be at your approach speed (called Vref). So final approach speeds are also between 130 - 150 kts.
What is a typical VNE at 1000 feet altitude?
Most modern airliners have a lower level Vne of between 330 and 350kts. It will not be exceeded by line crews during normal operations and we don't consider any safe margin beyond Vne.
Is an airplane able to fly as fast at sea level as it can at 35,000 feet? If not, how much slower can we expect to fly at sea level?
This is slightly more complex. Aircraft are limited at the higher levels by a Mach limit (called Mmo). This is due to compressibility effects at high Mach numbers. It is usually in the region of M.78 to M.88.
It would be easier if I answer your question by working in TAS (True Airspeed). At the lower levels TAS is close to IAS (Indicated Airspeed). Vne is an IAS limit, so max TAS at lower levels would be between 330 - 350 kts.
At altitude, TAS would be around 430 - 480 kts, so in still air, the aircraft would be over 100kts faster at altitude.
Somewhat off the subject. At altitude you can get winds of over 150kts, so it is conceivable that an aircraft at altitude with a strong tailwind could achieve over 600kts over the ground.
Like I said, this is a slightly simplified version of the true physics involved, but good enough for your argument.