Your radiation pattern from an omni antenna would look like a beach ball with a weight pushing down at the top making the top and bottom flat. Tilting the antenna lifts one side of the ball but pushes the other side down reducing signal strength to the horizon. The side pointing up will send more signal toward clouds and possibly also reducing signal strength at te horizon. The best result is keep the antenna vertical and increase height.
Rept18 should be the correct slot for the site you are trying to access. The question I have for you is what mode are you using to send the tone? If the repeater uses the same tone both in and out, the Tone Squelch is the correct entry. If the repeater uses only a receive tone, the you need the tone on your transmit and the mode as Tone.
There's a few tools you will need to troubleshoot the issue. The one to start with will be a multimeter to measure voltage and current. The second is Ohm's Law, knowing how voltage, current and resistance interact. Dividing power (watts) by voltage tells you the current (amps) available.
I only know of one radio that comes with an N connector as its output. Using adapters is common and they don't really add to any loss figures so an N female to PL259 or N male to SO239 adapters are fairly common. They are a little on the pricey side compared to the normal PL/SO adapters but I believe that is due to the number of connectors sold rather than the manufacturing costs.
Yes - it's called in your pocket.
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Shop around for a coordinator. The FCC lists the authorized coordinators on its website. If you deal directly with the coordinator you save any dealer markup.