For example, if the taxi fare is 53 THB and I give 60 THB (for lack of coins), the taxi drivers typically will not give any change back. I wonder whether this is because I don't look Thai or because it is the tradition here for taxi fares not to give change back if below 10 THB.
According to TripAdvisor, in taxis, "both Thais and local ex-pats commonly round up the fare (i.e. 51 baht fare rounded up to 60 baht)." As ฿7 is equivalent to US$0.22, I wouldn't worry about it much.
Tipping is not necessary but it’s common to round up to the nearest 5 or 10 baht.
The same page also gives some interesting advice regarding the case where the taxi driver claims not to have any change (which in my experience does happen once in a while, even for 5 THB change):
I’ll warn you that if you use a taxi without having 100 baht notes or smaller, you may have trouble getting change from your driver. It’s common to claim “no have change” – and I’m not sure how you’re going to prove that they do. I’ve asked to drive on to a 7-11 before so I could get change – suddenly the driver found some coins in his center console.
Take a selection of 100 and 20 baht notes plus some coins if you want to pay the exact fare.