Learn Turkish: Keşke hafta sonu serbest olsak. - I wish we were free on the weekend.

The word keşke (if only / I wish) pairs with the conditional suffix -sa / -se to express a strong wish about a situation that isn't currently real. Here, ol (to be) + -sa (conditional) + -k (we) translates to 'if only we were' or 'I wish we were'.

Where does the 'I' in 'I wish' come from, since the verb olsak ends in the 'we' suffix -k?

The feeling of 'I wish' is packed entirely into the word keşke (which can also mean 'if only'). You don't need a separate verb for 'wish' conjugated for 'I'. The verb olsak provides the 'we were' part of the sentence.

Could I use bedava instead of serbest to say 'free' here?

No, because bedava means 'free of charge' (costing no money). When you mean 'free' as in having free time or being unrestricted in your schedule, you use serbest. You will also commonly hear boş (empty) or müsait (available) used in this context.

Why is there no 'on' or 'at' suffix on hafta sonu to mean 'on the weekend'?

In Turkish, common time expressions like hafta sonu (weekend), sabah (morning), or days of the week can act directly as time adverbs. You usually don't need to add the locative suffix -nda / -nde (in/at/on) to say 'on the weekend'.