First off, hypothyroidism may account for an average of 5-7 pound weight gain -- despite what people claim -- and most of this is fluid retention. There can be more severe cases. So, the thyroid is likely only part of the issue with weight.
with that in mind,
1 -- somewhat low dose for a 24yo healthy person, but this needs to be individualized
2 -- the response to meds may take 2-3 months overall, and it may not involve weight loss
3 -- some do report weight gain, but this is not common. Likely due to appetite stimulation
4 -- no, but avoid generics
5 -- not likely related, but some people are sensitive and take 10-14 days to get used to the medication -- if these symptoms persist, you may need an even lower dose
If you took your med at 9 a.m. and felt poorly at 7 p.m., I don't think it was the medicine. You may not have eaten enough during the day, or since your thyroid affects pretty much every metabolic process in your body, working out may have pushed it (thyroid) past its ability and you were working off your adrenals. You may have to bring your workout down a notch or two until you are feeling better.
Hang in there. It's incredibly easy to be paranoid and anxious right now. But gather as much information as you can and don't be afraid to ask your doctor questions. They are under rigid time restraints from the insurance companies, but if you are organized and have a list of questions ready at your appointment, you can usually get the answers you need.
I found these websites very informative:
www.thyroid.about.com
www.mythyroid.com
www.thyroid.org
and Mary Shomon's book, "Living Well with Hypothyroidism."
Good Luck!