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No. As you found out there is no way to read the contents of the furnace.
Yes, but the details of the implementation will depend on what you are trying to do - e.g. should the countdown continue if there is no iron in the furnace? Can we assume that input is always satisfied or do we need to guard against empty inputs, etc?
What are you trying to do?
Edit to add: This will remove one iron output at most every 50s
What I'm thinking, is you could use the inserter feeding iron into the furnace to count inputs. An arithmetic combinator with its input connected to its own output and set to "Everything + 0" will serve as memory. The inserter putting the iron into the furnace is set to read hand contents, so each plate it puts in will be added on the combinator. Then the output inserter is also connected to the output and set to operate if the iron plate count is >= 65 (13 * 5 iron per steel). Then you would need another circuit to reset the count. A decider combinator could momentarily interrupt the arithmetic's feedback, on the condition that the output inserter is reading >0 steel plates.
Of course, if it's an electric furnace and you put productivity modules in, then that will screw up the ratio so you'll have to change the condition value.
Personally, I would keep a countdown which is incremented by however long it takes ot make one steel for every five iron plates picked up, and then trigger the steel inserter if the count is 13 and the countdown is zero.
The input inserter will only stack up 10 iron plates on the furnace's input que (2 batches worth). After that it will wait until a new batch starts before putting in 5 more. If it's benefitting from a stack bonus, it might put in more than 5 at a time in which case it will still wait until there are <10 plates before operating again.
If you set it up this way the *first* time the output inserter operates it will have less than a full load, but every time after that it should grab a full load.