How do I test how many amps a transformer actually puts out
If it's rated at 3.3A and you draw much more than that from it for an extended time, it will exceed its rated temperature and eventually its insulation is likely to break down. At which point, smoke ensues.

Whether 20% overload (4A) is too much more I can't say. I would guess short periods of operation (up to an hour, then cooling down for an hour) would be OK for my own use, but I wouldn't sell anything made that way. 

7 amps is definitely too much.