Do you have to pay to get your show on air?
You "can" buy airtime, which is what INFORMECIALS do. On Cable and local broadcast, you can sometimes buy 30 minute or 60 minute blocks of time and put a show on TV, as long as it still follows FCC laws on restrictions of content.
Most TV series however are purchased or produced by the channels.
Does the channel station automatically put in the commercials for you?
They are buying the right to air the show for a limited time period and sell the commercials for that, although a lot of national shows come with pre-sold money from an "anchor" sponsor, like car companies that are advertising nationally, then several "spots" are sold for local markets.
About how much profit does the channel station get and how much profit does the TV show get?
Define "profit".
A 30 minute show is usually 23 minutes of content so you have 7 minutes of commercial time = 14 of the :30 second commercial slots. They sell those for as much as they can, and hopefully make more than 2 times what they paid to broadcast the show.
Shows with higher ratings, meaning more people watching = ad time is worth more $$$ to the advertisers because they will reach more eyeballs.
Also there is PAY CABLE, like HBO and SHOWTIME with no ads because people pay a subscription fee to the cable company each month that pays for their original programming.
This might be easier if you stated what it is specifically you want to do. A sitcom? A reality show? A drama? Who is your intended channel?
and CF's sketch is freakin' brilliant.