Question about trills

Trills have length same as the dotted note, but do trills have rules of how many times do repeat, or it is as fast as you can during that period?

Actually I play trills as fast as the period is .. [With NO RULES]
I don't know if theres any rules for trills ??

There is no rule about the number of repetitions. You decide the trill's speed, it's a matter of taste. It's not always to be played as fast as possible (can be slowed down for lyrical effect), nor is it always to be played rhythmically (can be meant to be heard as a "line" rather than a lot of repeated notes).

My challenge in playing trills is that I like them to sound "liquid" and "light" --mine tend to sound "laboured" and "heavy". When I do manage to get the light liquid sound, I am delighted, but most of the time I am very unsatisfied with the sound of my trills.

To make them sound "liquid" as you say, you have to use your fingers only, without any weight. Try to play EXTREMELY slow trills (1 note every 2 seconds is the max. speed) as pianissimo as possible, using just your fingertips: try to feel the impact point of the hammer on the string every time, then speed up VERY progressively.

In one of my videos on youtube, I improvise and play a very long trill at one moment: https://www.youtube.com/watch?v=8ukO7bNFdsI

Thanks for the help Matthieu - I checked out the video clip you suggested -- wow that was a long, long trill. Very impressive. Plus you trill with your 4th and 5th fingers,not just your 2nd and 3rd fingers -- definitely still a big challenge for me. I can manage 1 and 3 or 1 and 2 or 2 and 3 but getting the 4th or 5th (pinky) in the game and things start to fall apart..

I'm still trying to figure out how to play a trill that's a slow as you suggest -- as you said

"(1 note every 2 seconds is the max. speed) as pianissimo as possible, using just your fingertips: try to feel the impact point of the hammer on the string every time, then speed up VERY progressively.[/quote]

but I'll give it a try. I suppose the action of the piano might affect how easy this is to do too. Lots to try and think about.