This FAQ on issues embedding forms will give you some guidance on how to embed the form in your own website: http://forums.adobe.com/docs/DOC-1991
As far as Printing, there isn't any support to print the form from the web browser, but in a Paid level subscription one of the features is the ability to download PDFs, including "Download response as PDF form" from the View Responses tab for any response/submission, this will download a filled out PDF that looks like the original form (some things can be moved around to accomodate printing such as text fields expanding if text does not fit. This downloaded PDF will print well.
You might want to look at this discussion for more background information on this user's problem: http://forums.adobe.com/thread/1447097?tstart=0
There was apparently a problem with check boxes printing, though the details are lacking...
I responded to another post of yours today pointing you to the instructions for designing for PDF so you can define the page breaks that will be used in the PDF. I would guess that the issue with the checkboxes is also related to overflowing text input field, if the checkbox allows "Other" and the users input is larger than the input box then it will take up it's own row just like the text fields do.
You are welcome to share your form with me and I can test the PDF output (let me know a specific response you are Downloading as PDF form so I can reproduce what you see):