Japanese clans can't declare war on someone outside Japan until they unify Japan. Annex the other clans to unify Japan.
It's been done, but it isn't easy.
Send other countries gifts of money to improve your reputation with them. Other things like Royal Marriages and Alliance also improves reputation.
Your Heir's claim to your throne. Don't worry about it too much unless you have a lot of Royal Marriages.
Yes, Trade Agreement is a diplomatic option you can have with Countries. I don't think Japanese Clans can, though. You're pretty much locked out of the rest of the world until you unite Japan.
Stop minting, hire Masters of the Mint or take the Idea of National Bank to reduce it.
Don't play Japan. Play France, Castille, Austria. Someone big.
Every question you asked could have been worked out on your own if you'd bothered to look around a little.
Read the manual and read the
EU3 wiki. The manual can be downloaded for free, just google it.
If you're still stuck, then you should be asking others.