I don't see the contradiction/weirdness in both wanting to be like someone and being in love with someone (or, like you put it, wanting to do someone and wanting to be someone); after all, don't a lot of us fall in love with people we admire? There's a fine line between hero worship and crush, etc etc.
About Nightwing being Devin Grayson's Mary Sue, I think you're right on the money. In one interview where she was questioned about Tarantula being her Mary Sue, she answered that she thought it'd be much truer to say that Dick was her Mary Sue. Incidentally, I'm not sure if she really understood what the term 'Mary Sue' meant/means/is used as, in part because like batcookies said, it's used any way nowadays. As far as self-inserts go, however, I'd say her most probable self-insert was Babs. Her Babs says a lot of things, particularly about people's psychologies, that seem to reflect how Devin Grayson intended the portrayal to go. Sometimes it reminds me a little of how Hermione was depicted in Harry Potter.
...And as for objectifying Nightwing's character... she's not the first nor the last writer to have had characters remark on him being beautiful.