All iPads are sold unlocked, so yes you can use any iPad sim card. Although the Verizon 3G iPad doesn't have a sim and will only allow coverage in certain countries.
The IPad Forum is a community of members from all walks of life and from all over the world coming together to share our experiences and to help each other learn about this wonderful piece of technology the Ipad. There is a wealth of information already here in the many threads we have so doing some searches will answer most of the questions you have. If then you cannot find the answer you are seeking then by all means post your question. There are many friendly and informed members here only too willing to help you.
Some iPads are sold locked to a carrier, like by Orange in the UK. They're sold subsidized by carriers, so they are locked so the carriers can make their money back.
Not sure how you can tell, other than by trying a SIM card from another carrier.