First, one does not control the other. Many times one party says "if you go after child support, then I'm going to go after sole custody of the kid, so there!" This is baloney. Its popular advice in bars (the kind where you go to unwind) but it doesn’t work in the courts.
Child support is required in all states. It depends entirely on the amount of time the child spends with each parent, what expenses each parent pays separately, and how much time the child spends with each parent. There is actually a formula, you put in those numbers and the computer gives you a presumptive chlid support level. The judge can vary it for different reasons (like intentional 'underemployment').
Parenting time is the time each parent gets to be the parent with the child. It doesn't matter if you haven't had contact because the mother barred you from contact. However, if you wrote a letter and said "I want nothing to do with the brat" then that might influence the court's decision about giving you parenting time (but only the amount). The law presumes that each parent is entitled to 50% of the parenting time. Where you live in different states that formula is usually handled with summers, holidays, etc., and the order will include who pays for travel, who travels each direction with the children if they are too small to fly by themselves, etc.
Finally, the issue of paternity. You have the right where a demand is made for child support to obtain a paternity test to determine if the child is yours. If the child is born during marriage, it is presumed to be yours. However, if there is no marriage and the child is not yours then everything I said above applies to the real dad.
Finally, finally, a parent’s personal conduct is only relevant to you if it impacts their fitness to be a parent. Here you have to decide, is the child better off living with me (and am I better off having a full time baby on my hands) than living with the other parent, even if only part time, who is engaging in whatever behavior that you don’t like. Some behaviors, like dating new partners and having them sleep over is probably not going to interest the court into changing anything. On the other hand criminal conduct, drug abuse, these things will cause a court to change the current situation. That's for you and your lawyer to discuss.
Some attorneys sell unbundled legal services where you pay for just what you need and can afford. For example, some attorneys will give you an hour or two at a set price to review your lease and give you advice based on the law, prepare letters for you to sign, or sell the paperwork for the court filings; then you can proceed on your own, but knowing that your paperwork is correct.
Good luck. jim
NOTICE— The Legal Information contained in this answer is provided solely for informational purposes to assist the layman with understanding legal issues, and is not legal advice nor intended to create an attorney-client relationship between you and me or my law firm. Such Legal Information is intended for general informational purposes only and should be used only as a starting point for addressing your legal issues. It is not a substitute for an in-person or telephone consultation with an attorney licensed to practice in your jurisdiction about your specific legal issue, and you may not rely upon such Legal Information. You understand that questions and answers or other postings to the Site are not confidential and are not subject to attorney-client privilege.