No, a negative Fst value does not necessarily mean there is a concern for inbreeding depression within the population. Fst is a measure of genetic differentiation between populations, and a negative Fst value indicates that there is less genetic differentiation between the populations, which can be explained by gene flow, or other factors such as selection. However, a negative Fst value does not indicate the presence of inbreeding depression. To assess the risk of inbreeding depression, one would need to measure the amount of inbreeding within the population.
Agreed but with an extra caveat. Theoretically Fst can only range from 0 to 1, with 0 indicating identical allele frequencies and 1 fixation for different alleles. Negative Fst values can be an artifact of the algorithms used to calculate Fst from genotypic data. I would interpret a negative value as essentially being zero.
A more informative measure for inbreeding is Fis, which measure excess vs. deficiency of homozygotes based on allele frequencies.