Clarification:

Firstly, you are correct in stating that sharpness is subjective, but the ability of a camera system to resolve small details can be measured, and this measurement is strongly related to the perceived sharpness. As you image black and white lines that get closer together they will eventually merge into a grey blob. By measuring how close lines can get before a losing a certain amount of contrast between the black and white, you get a measurement of sharpness. Expressing the distance between the lines relative to the picture height removes the final output size from the equation, this the sharpness measure is maximum line-pairs (i.e. one white one black) per picture height that have enough contrast to be distinguished.

1st question:

All things being equal (same lens, subject, settings, final output size) the larger sensor will produce an image with higher peak sharpness in the centre of the frame, and higher average sharpness across the fame. It may have softer corners than the smaller sensor image as the sharpness of the image circle projected by the lens can drop off significantly the further you move from the centre, and the larger sensor captures the extremes of the lens image circle.

If you take for example the 8mp Canon 30D and the 22mp 1DsMkIII, the 30D has almost exactly the same pixel size so it's image is akin to cropping the middle out of the 1Ds image. As you can imagine, cropping the middle out then blowing the image up to get the same output size, you will have to upscale and lose sharpness.

If you take for example the 12mp 450D and 12mp 5D, the smaller 450D has the same number of pixels but they are much smaller and together take up less of the image projected by the lens so it's sort of like blowing up the centre of the image projected by the lens, again losing sharpness. The bigger pixels of 5D sensor effectively view the lens image from further away and are less demanding of the lens resolution and will thus produce a sharper image.

You can see this trend for larger sensors to produce sharper images reflected in the dpreview lens tests, which allow you to see the MTF (a measure of lens resolving power, or sharpness) of the same lens on different sensors:

http://www.dpreview.com/lensreviews/nikon_50_1p4g_n15/page3.asp

Compare the test results of the Nikon AF-S 50mm f/1.4G lens for the DX (1.5 crop) format compared to the FX. At f/4 the DX (smaller) sensor resolves 1500 line pairs per image height in the centre, and 1250 in the corners. The FX sensor, at the same aperture resolves over 2200 lp/ph in the centre and over 1500 in the corners!

2nd question:

For your second question increasing the number of megapixels for the same sensor size will improve sharpness (then thus image quality). However the improvements get smaller as the megapixel counts increase, thus at some point you need to move to a larger sensor. It's hard to say whether the D7000 will meet your sharpness needs, you'll have to try and borrow one!

There is another factor which makes much more difference than sharpness between sensor sizes and that is depth of field. Again, all things being equal (most importantly framing) you will get shallower depth of field with a larger sensor, around 1.3 stops. For most people this is a major reason for using a larger sensor 35mm DSLR. To get the same image as a FF camera shooting at 50mm f/1.4 on an APS-C (like the D7000) you would need something like a 30mm f/0.9, which doesn't exist!