When I forward my .ai file for printing, the font is changed on the printer's computer. How I can solve this problem?
If I sent an .ai file the font is changed, but if I send a .pdf file the resolution doesn't match.
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Don't send a native Illustrator file. The reason the font is changed is (most likely) because they don't have the exact font installed; Illustrator files don't embed fonts.
Send a PDF file, which is the standard for sending files for print and shouldn't give you any problems with missing fonts.
As for your resolution issues; any vector artwork will remain vector and any raster images will be resampled and compressed based on the settings you choose in the PDF save dialog (which you can set to not resample or compress at all of course).
The relevant options are under the "Compression" tab; As long as your document is at actual size and you set the downsampling to no less than your printer specified then you shouldn't have a problem (assuming you're images were ok to begin with).
Of course, if you're still having trouble with embedding fonts you can outline your type which will convert them to vector shapes.