In Pearl I somehow raised my Happiny's Happiness to MAX,holding the oval stone and it evolved into chansey.After the evilution I raised Chansey's level by 1 and it evolved into Blissey.Is this Normal ?
Happiny doesn't need to be happy to evolve, it just needs to be holding the oval stone when it gains a level: but only during the day. You may have made it happy by raising it, but it wouldn't evolve if you were raising it at night. Chansey on the other hand DOES evolve with happiness
conclusion: happiny was already happy enough when it evolved to evolve again straight away
Yes. Perfectly fine :D
That Happiny had obviously fulfilled the happiness reqirements to evolve into Blissey before it evolved into Chansey, or on the level it did. So therefore, if that is the case, this is perfectly fine.