… can I use the old lenses with this new model?
Yes. The 7DMkII is a "crop" box, so it can use both EF and EF-S lenses. This is only if you switch to a full frame box like the 5D / 6D models that you can no longer use EF-S lenses.
And if so, what quality will I lose by doing it?
Since these two lenses are considered entry-level kit lenses, it is unlikely that you will lose a lot of quality because there is not much quality to lose. 😉 However, given the improvements made to the processor and sensor between the 300D and 7DMkII, it is possible that the number of faults is much higher. Increasing the resolution from 6MP to 20MP, in particular, may indicate some additional drawbacks of the lens.
in addition both of these lenses as entry-level lenses have been replaced during the last decade. The objective of the current 18-55 kit is probably the fifth or sixth iteration of this lens and is now equipped with both stabilizer and stabilizer. And the 75-300 III has been replaced by three lenses: the EF-S 55-250 IS (low-end entry-level), the 70-300 IS USM (medium-quality, improved optics and updated system compared to the 75 -300 III IS USM) and IS USM 70-300L (superior quality, improved optics compared to 70-300).
And to top it off, none of your goals are particularly suitable for shooting sports, which is not an entry-level subject. Sports tend to require autofocus speed. To do this, the 7DMkII can certainly work on the body side, but you will usually want a ring type USM lens for the lens side (with the video, STM may be more useful; slightly slower, the focus be smoother). And if sports are indoors or at night, you will probably want as wide a goal as possible. opening possible. And the good telephoto zooms that do that on the Canon fence side tend to be white and cost four digits. Sports and wildlife are two areas in which the costs of equipment are not modest.
Stabilization may or may not be essential, depending on the length of your lens, the lighting conditions for the sport in question, and your intention to shoot video or still images. With video, IS can help mitigate the pan. With still images, the sport usually requires higher shutter speeds to "freeze" the action. You may be more than 1 /focal distance (a general shutter speed target to mitigate camera shake blur; that is, with a 300mm lens, you want to be more faster than 1 / 300s), anyway. If we are talking about football, a 75-300 may be suitable. But indoor hockey, swimming or basketball, probably not.
It seems that the difference of mm67mm could be important too?
Well, it just means that you can not use the 58mm filters you already have without vignetting. You will need to purchase 67mm filters, but with a reduction ring you will be able to use 67mm filters on your other lenses without vignetting. Of course, if you end up having a white L lens, it is likely that you will need filters of 77 mm (or more).
If you want to reduce repeat filter purchases, purchase the largest size you need and then the appropriate reduction rings. Unfortunately, the larger the size of the filter, the more expensive the files.