Learn French: Combien de choses choisissez-vous pendant les soldes ? - How many things do you choose during the sales?

After expressions of quantity like combien (how much/many) or the ones from this lesson like tant and tellement (so much/many), you just use de or d'. You drop the plural article les, so it becomes de choses.

Could I ask this question without using the inverted choisissez-vous?

Yes! Inversion is the most formal way to ask. In everyday spoken French, you will often hear Combien de choses est-ce que vous choisissez ? or keeping the statement order: Vous choisissez combien de choses ?

Why is there an -iss- in the middle of choisissez?

Choisir (to choose) is a regular -ir verb. These verbs add an -iss- before the ending in all plural forms (nous, vous, ils/elles). So for vous, it is chois-iss-ez.

Does les soldes mean 'sales' as in a company's revenue?