There is a "sticky" that will help you to start;
http://forums.trailerlife.com/index.cfm/fuseaction/thread/tid/17730894.cfmIf your brand of hitch is not listed I would suggest an internet search for it and read what the specific maker recommends. The same thing applies to the friction sway control device as you were lacking and some adjustment is possible.
Some of what you describe is normal and the product of physics but it can be improved. There are also better hitches available than what you were provided. There are several choices in integrated WD/sway control hitches that are popular with forum members including me that provide much better performance.
As to the nose high or low, level is the desired position but if that is impossible slightly nose down is preferred and can have significant impact on the trailers behavior.
Concerning the tires, LT tires can make a big difference but you must ensure your wheels are compatible as well.
ST trailer tires have a max speed limit of 65 mph and that is another whole discussion.
You have much to learn but you have come to the right place.