Learn French: Nous préparons un grand gâteau avec beaucoup de fraises. - We are preparing a big cake with a lot of strawberries.

No, and this is a strict rule in French! When expressing a quantity with words like beaucoup (a lot) or un peu (a little), you always use just de (or d' before a vowel word), even if the noun that follows is plural. It is never beaucoup des.

Can I drop the de and just say beaucoup fraises?

No, you always need the de. Think of it like English: we say 'a lot OF strawberries'. French requires that same connection. Beaucoup by itself just means 'a lot' (as in, je mange beaucoup = I eat a lot). When you want to say 'a lot OF' something, you must use beaucoup de.

Why is grand placed before gâteau? I thought adjectives went after the noun in French.

You are right that most French adjectives go after the noun. However, a small group of common adjectives describing Beauty, Age, Goodness, and Size go before the noun (sometimes called the BAGS rule). Because grand describes size, it comes before gâteau.

The translation says 'we are preparing', but where is the word for 'are'?

French does not have a separate 'am/is/are doing' tense like English does. The single present tense verb nous préparons translates to both 'we prepare' and 'we are preparing'.