If I run a Tor relay in a machine and at the same time I use the same instance as a Tor client, would that harm my anonymity ? Would it be better to use different Tor instances on the same machine? Are there other implications ?
No, it won't hurt your anonymity and there are no other implications (unless you're severely bandwidth or CPU constrained). Obviously running a relay requires a bit more bandwidth and Tor can be a bit of a CPU hog but any semi-modern processor should be able to handle the extra load fine.
I should note that running a public relay does let people know that you have Tor installed (not necessarily that you're using it). But anyone observing your traffic knows that anyways unless you're taking other measures to prevent that (eg. trying to disguise your traffic using one of the obfuscation bundles). This isn't really an issue (and not something Tor tries to protect against by default), but it's something to bear in mind.
It would not decrease your anonymity to run a Tor instance as a relay, while you are using it for your own purposes. It's possible that doing so would even increase your anonymity, since it would be more difficult to analyze your traffic patterns and timing patterns, which are two things that Tor does not hide very well from a sophisticated attacker. The reason for this is that the attacker may have trouble distinguishing your traffic from relayed traffic. Keep in mind, however, that this only works if your relay is being actively used by other Tor users. You can see this in Vidalia by clicking on Bandwidth Graph and observing the bandwidth usage while you are not using Tor for anything.