Some questions:

1. "I always thought it would be better to be fake somebody than the real nobody". And, in Dikkie, a socialite snob from the money and status rich Greenleafs, Tom just found a true blue catch; someone he could immediately see himself as. He wanted it and the pretense started right away. Not to mention that happened when Meredith noticed his pitiful one suitcase under 'R'. The fake someone switched right into his new character; someone fake that was exactly who he wanted to be: someone impressive. So he introduces himself to impress Meredith.
2. It was so that Marge would still believe that he was alive, yes. She didn't believe Tim and Meredith makes an impressive witness. And the lie was that much more credible with a bit of a sting as coming from a beautiful, rich socialite Logue; the girl whom he allegedly dated. Morevore, it's coming from someone as far away from Tom (as she thought). Marge was to believe it immediately and moreover stop further inquiries into Dikkie's disappearance. That's a major victory for Tom. Also, as an added bonus, it keeps Meredith believing that Tom is indeed Dikkie and also makes him even more desirable to her. This is important because Meredith loves drama and now she thinks she's in the middle of some ruling class love triangle. What heaven to Meredith Logue! And this is important to set up the ending.

3. As twisted as Tim is, he never really planned any of his murders; they all sort of fell into his lap with most of them happening when he's backed into the corner (or, locked in the cellar to make it more apt). Dikkie's was his first and also the only murder of passion. He loved Dikkie (or at the very least he admired him and wanted to be him). Ideally, he would have preferred to come back to Italy in the new year and share an apartment with him in Rome. Then, Dikkie went after him hard and mercilessly, taking no prisoners. Imagine someone you loved and looked up to as a god, really, then turn and call you a girl, a leech, glad to be leaving and wanting nothing to do with! Tom was both heartbroken, infuriated but most importantly - disillusioned. Because in his active and far reaching imagination, Dikkie was in love with him, too. They were gonna share their life together in the that Bourgeoisie apartment with fine things and class. Dikkie would give up the awful sax and take up piano. He'd break off with Marge finally and would never need another man or a woman after he'd realized how perfect Tom's love was and would be forever sweetly grateful from saving him from frivolous women, vile clubs and music and rude, opinionated friends (Freddy). He crushed the illusion, and exposed Tom for who he is, something that would truly make him stop, as Tom truly despised only one person: and that's Tom.

3. He wasn't going around playing a double for Dikkie. He only played Dikkie in person to those who gave never met him. And he was so good as being Dikkie that they took him on his word. Tom was better at being Dikkie than being Tom. Because, again, he was better being fake somebody than real nobody!

1. It's all but outright stated that on top of everything else, Tom is a pathological liar. And the thing about pathological liars is that they will lie even when it makes no logical sense to do so. As far as Tom knew, he'd never see Meredith again so to him, what's the harm in pretending for a brief moment that instead of being Tom Ripley the piano player and washroom attendant, he was actually Dickie Greenleaf the wealthy socialite and layabout son running from his responsibilities to live a carefree lifestyle in Italy? It's also implied that he'd already become somewhat obsessed with Dickie and/or his lifestyle through the research he'd done before leaving.

2. When he unexpectedly ran into Marge at the opera, it was clear she was getting suspicious. She had inadvertently caught Tom in a lie by discovering that he wasn't in Venice despite him announcing that was his intended destination, he looked unusually smart and wasn't wearing his glasses, and he seemed quite flustered when he said he hadn't seen Dickie. By setting up the meeting between the two ladies (and Peter) at the cafe, he managed to make Marge leave Rome by using Meredith to convince her Dickie was sorry for running away and was on his way back to their old home, as well as allaying any potential suspicions either of them had by (a) providing "proof" that Dickie was still alive and well and (b) "proving" that Tom Ripley and Dickie Greenleaf were still two completely separate individuals.