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Yes, those are generally signs that your male wants to mate with your female.
However, you mentioned you've only had them for eight months. Budgies should be at least a year old before you think about breeding, although it sounds like you don't want them to at this time.
You also mentioned that your female is sick--have you taken into the vet for a proper diagnosis?
By decreasing their daylight hours and rearranging the cage often, the male's want to be with the female should decrease. Additionally, new toys may help distract him if he continues to harass her.
For future reference, breeding does not guarantee eggs, and if it did, you can always remove the eggs as they are layed (life only forms after consistent incubation) and toss them to throw the hen out of her laying cycle.
As for right now, and because of the added stress of an illness, it may be best to separate them for the time being so the male doesn't wear her down if he's persistent.
If you would like to breed your budgies when they are both at least a year old and in good health, be sure to do plenty of research beforehand! Here on the forums there are scores of informative articles
I hope that helped a little bit
We'd love to see your little birds when you get a chance, and it's great to have you join us here on the forums.
Hope to see you around and good luck!