I have started a site, ran it for a year, sold it then tried something new (freebie related) and found out it didn't work well.. So here are my answers to your questions.
1. How much capitol do most sites need to start? Need: Just enough to buy a script and pay for hosting (~$600).
However, I would highly recommend having ~$5,000+ (ideally $10,000) to get started, as well as a day job, so you can afford to give the site time to grow. This pool of funds is in addition to the start-up script costs.
2. How much does it cost to get a custom script and where can I find someone to do it for me? Custom.. Depends upon the quality of script you want, most likely $10,000 for it (this includes a quality script plus solid design).. However, I highly doubt you know all the features (security/administrator/automation/etc) that you want included, so it may be easiest to buy a canned script to take a look at and go from there..
3. How long does it take for most affliate sites to pay the owner/owners of an incentive site? Typically NET30, occasionally NET45, rarely NET15, and even never in some cases (revoked credits or shady owners [see midfielder100's nexus leads as a bad affiliate site]
4. Can I advertise offline as well? You can advertise however you would like. It would be your company. However, offline advertising is expensive and imo conversion rates are very poor for a website. BUT, it does build a brand name (but a brand name doesn't necessarily make you money)
5. I would like to sponser a forum like this one (if not this one) in turn for the same. How likely is this idea? What are you asking? You can advertise places like here if you would like. Almost every where has a going rate, typically on a CPM or fixed rate..
As others have said, I would not recommend opening a site right now. The competition is fierce and the advertising rates are low (trust me). You will spend countless hours in front of a computer, which can get mind numbing after awhile. Plus, it will take you several months of grinding to see any meaningful return on your investment (and this return won't necessarily be profit yet either). The accounting is difficult, since you never know when a seemingly abandoned account will finally complete and cash-out; and accountants are expensive (so are lawyers, programmers, graphic designers, and customer support staff). Also, the freebie enthusiasts are a little fickle, so one month business can be booming, but the next month you could be left wondering if anyone even visits your site. Plus, if you do open and then decide to close, the market is almost non-existent for defunct freebie sites, and people get very angry when you do not deliver on your promises, especially with money. Oh, and scammers are no fun (but I apparently am a 'tastey fet') and sometimes hard to catch (it's disheartening how base some people are) [and they make your advertisers pull leads, which makes accounting even harder]. That is why I would not get into running a site right now...
Oh, and I forgot to mention Taxes (just go ahead and write Uncle Sam a check for 30% of whatever you earn).
But, don't let me stop you from launching one if you want to. Just be ready to actually work (managing freelancers can be hell too).

-Joe