Flot will happily draw everything you send to it so the answer depends on the browser. The excanvas emulation used for IE (built with VML) makes IE by far the slowest browser so be sure to test with that if IE users are in your target group (for large plots in IE, you can also check out Flashcanvas which may be faster).
1000 points is not a problem, but as soon as you start having more points than the pixel width, you should probably start thinking about downsampling/aggregation as this is near the resolution limit of the chart anyway. If you downsample server-side, you also save bandwidth.
You can grab the image rendered by the canvas element used by Flot as a PNG or JPEG (remember to set a background). Note that it won't include anything not drawn in the canvas (such as the legend). And it doesn't work with excanvas which uses VML, but you could try Flashcanvas.
It's not really possible to determine the bar width automatically. So you have to set the width with the barWidth option which is NOT in pixels, but in the units of the x axis (or the y axis for horizontal bars). For time mode that's milliseconds so the default value of 1 makes the bars 1 millisecond wide.
Yes, Flot supports it out of the box and it's easy! Just use jQuery instead of $, e.g. call jQuery.plot instead of $.plot and use jQuery(something) instead of $(something). As a convenience, you can put in a DOM element for the graph placeholder where the examples and the API documentation are using jQuery objects.
Depending on how you include jQuery, you may have to add one line of code to prevent jQuery from overwriting functions from the other libraries, see the documentation in jQuery ("Using jQuery with other libraries") for details.
Flot is using standard HTML to make charts. If this is not working, it's probably because the framework you're using is doing something weird with the DOM or with the CSS that is interfering with Flot.
A common problem is that there's display:none on a container until the user does something. Many tab widgets work this way, and there's nothing wrong with it - you just can't call Flot inside a display:none container as explained in the README so you need to hold off the Flot call until the container is actually displayed (or use visibility:hidden instead of display:none or move the container off-screen).
If you find there's a specific thing we can do to Flot to help, feel free to submit a bug report. Otherwise, you're welcome to ask for help on the forum/mailing list, but please don't submit a bug report to Flot.