What am I looking at here?
You are looking at excerpts from a balance sheet. It is far from a complete balance sheet, as many items are missing.
What is the difference between current liabilities and long-term liabilities?
Current liabilities are debts the company owes that must be paid in the next year (or rarely, the next operating cycle if that is longer). Long term liabilities are debts that are due in more than one year.
What is equity?
Tiptree covered that one well. It is the assets minus the liabilities.
Is that cash or actual equity in the company?
In a simplified sense, equity includes money transferred into the company for the original issuance of stock, plus all earnings (and less losses) from the beginning of the business, and less any dividends paid to shareholders. It has nothing at all to do with actual cash in the bank.
From this table can I determine how much debt the company is carrying …?
Yes. That would be the total of the current liabilities plus the long term liabilities. And as Tiptree again very correctly noted, current liabilities will include accounts payable, which are normal operating expenses which have been incurred but not yet paid. That may or may not fit the definition of debt you want to use for any particular analysis.
and/or how much cash the company is sitting on?
Nope. Can’t squeeze that out of those excerpts. But keep looking around in that 10k, as there will be a full balance sheet in there somewhere. That will clearly identify cash the company has on hand.
Good luck on your forays into financial statements. I think they are one of the major keys to understanding a company and it’s suitability as an investment. But then again, I’m a CPA (although no longer operating in the financial realm, but sticking to taxation) and find financial statements fascinating.