I've three and a half years running now, and I have achieved two of these (the 5 and 10K ones). I recommend regular timed runs: parkrun - a target every week.
I reckon the marathon target is the most difficult of those targets, incidentally, but we are all made differently.
If it is a pool-based tri (I'm guessing it is), then you will be set off in waves. Once you are out of the pool, no one will know what position you are in, so no stress there!
A 4 week plan isn't going to do much in terms of improving fitness - most plans are at least 12 weeks and more often 16 weeks. If you are looking to get used to the discipline then do some brick sessions (bike then run).
I wouldn't worry abput separate cycling shoes. Just cycle in your running shoes-transition 2 will be very quick. Get to the event in plenty of time to register and get your bike in transition.
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