For the pyrantel, 1 cc per 5 pounds of cat. Repeat the dose every 2 weeks until he has had three doses. You can buy a syringe, at the human drug store. The syringe will say "m;" or "cc" on it. The average cat weighs 9-10 pounds. So you should be able to give 2 cc of the pyrantel.
Heartworms in cats, can cause a number of signs. The most common sign is chronic vomiting. But with heartworms, they do not vomit up the worms because the worms are in the lungs. Not in the gastrointestinal tract. So, from what you have described so far, I do not think it sounds like heartworms. Heartworms can also cause coughing and difficulty breathing.
Yes, you can give heartgard as a monthly heartworm preventative.
It is fine that you are not having an x-ray done. The cat is lucky to have you and is thankful for all the help you have given it already.
If you take a picture, of the genital area, I should be able to tell you if it is a male or female. To post the picture on here, use the icon, on the tool bar, that looks like a "paper clip"