It might last a little longer than fresh basil leaves that aren't made into pesto would last, but since it's not cooked I wouldn't count on it.
No - unless the label states "keep refrigerated" which should mean that it was in the refrigerated case when you purchased it.
Yes. Homemade gravy can spoil.
No it doesn't, but you can refrigerate it if you want to.
It will last longer if it is refrigerated.
A high-speed blender with a sharp blade is the best type to use for making homemade pesto.
Yes, since there are no natural preservatives in pesto, it should be refrigerated.
Fresh eggs can be refrigerated for up to 4-5 weeks before they spoil.
Yes, they do.
Yes, homemade simple syrup should be refrigerated to maintain its freshness and prevent spoilage.
yes after a while. if you want it to last longerput it in the freezer
Yes, or it will spoil very quickly.
Refrigerated hard boiled eggs are typically good for up to one week before they spoil.