(1) Following on from seren... it is also possible that the race was exactly 10K, but your training runs have been a little longer. I'd say that the measurement of the race course would probably be more accurate than the measurement of your own practice run.
And anyway, it's normal for race-day adrenalin to speed you along, and this time difference can be biggest in newer runners... so it's not too surprising. That may well be the sole answer.
(2)How to achieve 59:59 in November? Well the most important training tip is to address your injury. You'll never beat the hour by limping round!
If you didn't have a niggle, then I'd be fairly confident you could make progress in the 5 weeks. If you've only been running 3 months, you're still in the phase where you can improve times quite quickly. Plenty of advice around on the net (just google '10K training plans' and adapt them for your situation. For me, it's a case of mixing up your training to ensure there are some short faster runs along with slower longer runs.
3) It's hard to say... but overtraining is a distinct possibility. I presume you carefully selected the right shoes, with the help of someone who really knows what they're on about. Get that injury sorted.. don't exacerbate it.
4) Good luck Enjoy it.