In English you would typically switch the two adverbial clauses, 'he reads in the library every day'. Is there a similar tendency in Hebrew, but to put time before place, or is it just random?
In short, it's not random. It concerns what linguists call 'information structure'. Changes in the order of information and linguistics constructions (phrases within a clause, in this case) can change the order in which ideas/conceptualizations are activated, presented, and/or referred to in the mins of hearers. Changes in information structure can occur, for example, depending on the degree to which a construction is established/fixed in individual language speakers and conventionalized among groups of language speakers, the relative accessablity of the information in a discourse (e.g., whether it's relatively new, old, or otherwise accessible to both the speaker and hearer, perhaps already having been mentioned or not), the relative salience/prominence of the information), and the function it serves (e.g., as in the case of 'topical frames of reference', which can introduce a new topic or reintroduce an already established on, as in expressions such as "Now concerning next week's meeting ..."). I can provide a link that'll provide more (and hopefully clearer) discussion later, if that'd help.
That should have been "linguistic constructions" and "in the minds of hearers". Usually I'd avoid writing all that from a mobile device.
I answered 'Every day he reads in the library' and DL said this was incorrect. Two issues here: first, in English 'every day' can come in a variety of positions in the sentence and placing 'every day' at the beginning is entirely natural. Second, outside the US, for example in Australia, we only use 'every day' as one word when it acts as an adjective - for instance, 'it was an everyday occurrence', or 'It was reserved for everyday use', etc. In other cases, where 'every' is the adjective qualifying a noun, two words would be used: so 'it happens every day', and definitely not 'it happens everyday.' This is the case here and as an Australian I'd never write 'everyday' as it appears in this example. I think this is very much an American usage. LATER: I see that 'every day' now appears to be accepted (at least in some of the exercises: thanks, DL!)