Learn Polish: Gdybyś rzucił swoją pracę, założyłbyś własny biznes? - If you quit your job, would you start your own business?

In Polish conditional sentences, the personal ending (like -ś for "you") attaches to the conditional particle by. In the "if" clause, by is built right into the word gdyby, so we add the ending there: gdybyś. In the second clause, the particle by attaches directly to the end of the verb założył, bringing the -ś along with it to make założyłbyś.

Why are the verbs rzucił and założył in the past tense form if this is a hypothetical question about the future?

That is the core rule for making conditional sentences in Polish! Whenever you use gdyby (if) or the conditional particle by (would), the main verb must be in the past tense form (specifically, the third-person past form). Even though the meaning is "If you were to quit..." or "would you start...", the grammar requires the past tense forms rzucił and założył.

Could I say twoją pracę instead of swoją pracę?

You would be understood, but swoją is much more natural here. Swój (and its feminine accusative form swoją) is a reflexive pronoun that means "one's own". In Polish, whenever the object being possessed belongs to the subject of the sentence (here, "you" are the one quitting "your" job), you should use a form of swój rather than twój or mój.

Does always mean "to start" a business? I thought it meant "to put on".