Yes, these fees are deductible.  I'm not sure if we are supposed to post links on this forum to outside sites, but there is a very good primer on ehow.com on this.  You can just go to the site and search for the article title 'Tax Deductions for an LLC Business'.  Good luck!

Here is how I handle things (I actually have two different LLCs).   I pay with company checks if I can, but if I use personal money I file expense reports and then reimburse myself.   Just follow standard procedures of any other 'real' company: 1- pay if you can with corporate funds initiallyif you can't do #1, then 2 - pay with personal funds, then record it on the books and reimburse   Pretty straightforward

You can of course continually inject new capital into your business.  You would normally put this into an equity account such as 'Owner's Equity Investment', which shows up on your balance sheet's equity section.  Debit cash, credit Owner's Equity Investment.   I believe my accounting terms are correct. :)  

Startup fees (Like organization Fees) are deductible and as was said keep your records and receipts

Pay it however you want - just keep good records of what they funds were used for.

Filing fees, and company setup fees, are mostly deductible.  You ask a good question on whether to pay your personal credit card bill (either partially or in full) from your business account funds.  The answer should be no, and here's why.   The easiest way to think about your business and your personal spending is like this:  Just imagine that your business as a company you work for and you are an employee.  The question you then ask yourself, 'Would my employer write a check to pay for my personal credit card for charges I make on behalf of the company?'  The answer is of course a no.     Businesses require written documentation of all expenses.  So what you need to do is 'send' a copy of your receipt to your business.  You would normally file a reimbursement form, but you may be able to sidestep this formality by simply writing down the reason for the reimbursement directly on the receipt.  Store this copy of the receipt in your files.  Then you write a check to yourself from your business bank account.  You then pay your own credit card using your personal account.   If you don't have money in the business account, then you inject capital into the business from your personal account.     The main point about keeping your business separate from your personal is that you need to keep detailed traces of where your money comes from and where it's going.  If you start paying personal things through your business account, you are more likely to be viewed as 'mixing funds', which does not look good on you.     Cheers!