Do I need to pay LLC taxes in Indiana?

You may have to pay a minimum franchise tax in Indiana because you formed your entity there. Otherwise, unless you have Indiana source income you...

How does each legal entity handle company income that is re-invested in the company?

If you "re-invest" capital into an LLC or "S" corporation, that will increase your capital account. As a result that will allow you to take out...

Requesting an S-corp status for an LLC, is it the same as making a 'subchapter-S election' for the LLC? I'm confused.

Yes. Those two mean the same. You file an IRS Form 2553.

It is extremely unlikely that filing a 709 will increase your chance of having an audit of your Form 1040.

What would be IRS Tax implication on receiving $25,000 as gift from non-US citizen parents from foreign country?

No IRS tax implications. Read the instructions to IRS form 3520.

Forming an advertising company that will pay most of it's income to other clients. How is this handled via taxes?

I am not sure what you mean by "pay most of its income to other clients." In the advertising business typically the agency gets paid a percentage...

Do you only pay SMLLC taxes in state of residency?

The short answer to your question is "not necessarily." The long and scholarly answer has been provided by the scholarly Mr. Corrigan.

Do capital gains count as income that can bump me up to a higher tax bracket?

A short term capital gain is added to your ordinary income and those dollars will be taxed at a higher rate.

Can my husband file income taxes separately, and claim our children for the child tax credit?

He can file his own tax return and claim the child tax credit.

What is considered individual income if we filed jointly for tax returns?

For income tax purposes you filed properly as a married couple jointly. For immigration purposes they want to know his individual income. You...