In the US and Canada, the white wire is universally the neutral.
The "hot" wire can be red or black, both are used. Maybe the manufacturer was able to get a good deal on red wire.
Yes. Connect Black to Black, White to White and bare ground wires together.
Connect black to black and white to white from the switch. Your old fixture may have had wiring for multiple bulbs so they could be switched separately.
As the power to the light fixture should be, and hopefully is off, it does not matter which you hook up first.
Just install the new fixture with black to black, white to white, and cap off the ground wire on the new fixture. It'll be fine.
If these are all the wires you have then this would be a great assumption. It assumes also that everything before the fixture is wired correctly and with commonly used color schemes.
If it is a simple light fixture it does not meter - the light-bulb is a simple element of a chain that can be connected both ways.
This sounds like a typical light switch connection that turns on an overhead light fixture. There are two pairs of wires in from the supply voltage and two pairs of wires out to the light fixture. The two white wires are connected together in the back of the box. These are the neutrals from the supply to the light fixture. The two black wires are the ones that get attached to the switch. Incoming "hot" to the top terminal of the switch and the outgoing black to the bottom terminal of the switch. If you just touch the two wires together as you explain in your question then the light fixture should come on.
Wiring a 2 wire fixture to 4 wire outlet depends on configuration of wires in outlet box. If you have 2 white and 2 black I will assume there are more lights controlled by the same switch. 1st scenario attach both black wires to black of 120 volt fixture. Attach both white wires to white wire from fixture. atach ground to box or ground wire. 2nd scenario attach white neutral to white from fixture, Attach black hot to white going to switch. Attach black from switch to black from light Fixture. If you need further help I recommend hiring a contractor. Take a look into contraxtor.com
At that point, you should verify the home wiring; make certain that the black wire IS, in fact, the "hot" wire and that the white wire IS in fact the neutral. If the house is wired properly, connect the new fixture with "black to black and white to white." If you aren't certain that the house wiring was done properly, contact a local electrician to perform the work for you. Connecting a light fixture improperly can be dangerous to you and to anyone who subsequently changes a bulb or otherwise comes in contact with the fixture.
If both wires are black then the one with the writing is the neutral wire. If the two wires are black and white then the white one is the neutral.
You would have to provide more info to be certain what your problem is. Typically a black and white wire would connect to the two wires on the light fixture. The fixture should also be controlled by a switch that "breaks" the black (Hot Wire) to turn off the fixture. If you have a volt meter you can see if there is 120Volts between the black and white wires with switch on. If there is a single white wire going to fixture (Neutral), where is the "black wires tied" to. Maybe one of the black wires has broken off the fixture.
if fixture has two bulbs then two blacks are hot wires. Two whites are neutral wires.