Is zakat obligatory on the money that the brother took and lost in the stock market, knowing that the questioner now only owns her salary and an apartment that she will receive after 6 months and for which she has installments?

There is no zakat on an apartment designated for living, even if its installments have been paid off. Zakat is not obligatory on salary until a full year has passed while it is at the nisab (minimum threshold). As for the money with your brother, the rules of zakat on debt apply to it: if your brother is solvent and not a procrastinator, the amount is subject to zakat as if it were in your possession. If a year passes before the installments are paid off, then the debt waives zakat under certain conditions. However, if your brother is insolvent or a procrastinator, there is no zakat on this debt until it is received, and it is subject to zakat for one year after its receipt.