I can't answer all you questions, but maybe I can pass along a little info to help you.
First off I am assuming that what you are trying to use is strictly some LEDs interconnected.
If it uses ICs to individually address each LED or run in special flashing modes, some of what I am gonna say won't apply. In future questions, I would suggest that you include info on what arduino model you are using and what you are trying to drive with it (specs or name of the LED strip or other component)
(1) You wouldn't want to use analog AND pwm, since you can control brightness by just changing the PWM
(2) Since this is a passive load (like a resistor), the .7A rating says that the max A that you can drive the strip with is .7a, anything else will be dimmer (but you may not necessarily notice the difference). Motors and other "active" loads can "pull" power but this load (LED) will only use what your give it.
Since it seems like you are trying to power the strip through the arduino, the question we need to ask is - how much power can the arduino supply through its pins? The answer is 40mA (see fsource). This isn't even half of the max rating of the strip! :(
For a passive load, you can hook it up and try to drive it and see if it is enough (I really doubt it), but with an active load (ex. motor), it might pull too much power from the microcontroller and damage it.
What you are gonna need to do is use the arduino to control something else (Transistor, op-amp, relay, etc). That item will switch the power to the LED strip.
(3) Sorry, I cant be of any help for this one. If this shield you want is for the same project, it may have the necessarily power control electronics on it. So I would first find the shield and then see what you are missing. See the second source for a good site with info on many shields.
Hope this helps.