By negligible I assume you mean non-coordinating/nonreactive? Typically halogen anions form bonds with various metals and functional groups through mostly ionic means. This means in most polar solvents (especially water) these compounds are highly liable. Fluoride's smaller size allows it to bond with much more covalent character than the other halogens - in particular is bonds especially well with silicon (such as would be present in glassware) - thus fluoride is much less liable and not "negligible".
Group two elements with their typical 2+ charges are even more likely to bond through ion rather than covalent means, beryllium's small size makes it an exception in much the same way as fluoride.
For your nitrate and nitrite question, the -ate and -ite endings in general refer to the oxidation number of the central atom. -ate denotes high oxidation number (if there are several high oxidation states the prefix per- is also used i.e. permaganate) and -ite denotes low oxidation numbers (for several low oxidation states the prefix hypo- is used i.e. hypochlorite). The common positive oxidation states of nitrogen are +7 and +3 therefore we name the compound containing +7 nitrate and the one containing +3 nitrite. In these polyatomic ions oxygen's oxidation number is -2. Really the only difficulty is only in the naming convenients.