Hey Abe.
The faster blinking rate is indeed because you've removed the rear turn signals. For longer component and wiring life, it's probably better to stick with the stock turn signals.
The starting problem is primarily unrelated to the turn signals (assuming you don't have a short somewhere resulting from these new turn signals). It sounds like a classic case of fouled plugs and wearing out the battery by riding the starter button too much. Here's what I recommend:
~Get a battery-tender or other trickle-charger to charge your battery back up.
~Once the battery is charged back up, turn the choke off, open the throttle all the way and press the start button for a few seconds to clear out your chambers and hopefully de-foul your plugs without having to take off your fuel tank/airbox to get at the spark plugs. (NOTE: When doing this you want to listen close and be ready to release the throttle immediately in case the bike suddenly comes to life.) Once you've done this for 4-5 seconds, let the bike sit for a few minutes and attempt to start as normal with the choke.
I would wait for a fairly sunny day before doing this and take it out for a longer ride--at least 10-miles at 100+kph. Starting a bike for 3-5 minutes a day with a choke, but with no load or varying rpm, is not the best way to spend the winter.
Good luck and let us know how it goes.
-CCinC
P.S. The headlight should come immediately as soon as the engine is running. If you don't feel confident in doing the above, there's no shame in asking the dealership for help. (Well, at least the shame is preferable to a bike that was ruined before you even got the chance to ride it.) Don't be afraid to ask the dealership for help too. You just paid them a good deal of money for that bike, so they'll probably be very cooperative and helpful.
