I would definitely adjust the valves to the correct specs. Use of the Choke (fuel enricher) is pretty common on these bikes but if it takes a really long time to warm up I would go through the carb. If the bike sat a while, It is likely that the carb needs cleaned. I personally would hold off on changing anything on the carb too much until it has been cleaned and run a bit. I would also check the intake boot for any cracks and make sure it is sealing well.
A weak battery shouldn't affect the spark, some people even run their TW without a battery.
It sounds to me like your handlebars may be bent. I would look them over to make sure. You can either bend them back somehow, replace them, or carefully choreograph a crash on the other side to make them match.
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