1) Is there a reason you would prefer we not see the sites in question? I ask because you ask about the possible impact/effect of trademark on the situation, and if you are talking about U.S. trademark law, the potential for confusion by consumers, dilution, and unfair benefit are issues that could come to bear - depending upon whether the two sites are are selling to the same market, similar/same product(s), and other such stuff.
2) The company names are most likely not the relevant issue here, though per item 1 above, they could be - again - what are the respective company names?
3) That's a good question for a trademark attorney, and IANAL. There are jurisdictional and geographical issues involved that likely require the attention of an attorney with expertise in this area. Given that the other site already exists (does it's publishing pre-date yours?), you may not even be able to trademark the name of the site) and while you can copyright your site, you can't "copyright" the "name" alone - that's not what copyright is for or how it works (again, IANAL).
4) That's up to you. What do want to accomplish by contacting them?
5) That's nice - at least you are both indexed by the search engine.
I guess what I don't understand is whether or not you feel the other site is is some way infringing upon your rights, and if so, in what way?