Multiple solid layers, each with masks, then adding an effect

There is a composite on original setting in Advanced Lightning. All you have to do is check that and you won't have to add another solid to the comp.  

If you use the standard Ligntning effect you need to put it on a Black solid and set the blend mode to screen or add.

Connectivity animation changes every frame. Just animating Connectivity by multiplying it by time is not going to make any difference, even if you multiply time by .0001. If you want to simulate a lightning strike then you'll have to animate other properties. To give you an answer to the timeing question we need to know what your are trying to achieve and what you have tried. Do that by sharing a screenshot with all modified properties of the layer revealed. Do that by pressing the 'u' key twice. 

What tutorial are you following. I can think of a dozen ways to create the exact same image you have in your screenshot without using masks on multiple layers. When you are having problems with a tutorial it is important that you share a link to the tutorial. Framkly, most of the newer tutorials on the web are prepared by enthusiasts and their workflows and explanations may not be very good.

As suggested, put the effect on its own comp-sized solid. Usually one would choose black as a color to be able to play around with blending modes without affecting the appearance of the rest of the layers, but by default Advanced Lightning simply replaces/ overrides all the original layer content unless you enable "Composite on Original", so it doesn't really matter. Slowing down the effect is not realyl possible. It's inherent in how real electrical arcs work. You may be able to work around this by pre-composing the layer to a composition with a different frame rate and then in the parent comp apply a Timewarp effect or similar to at least get some form of interpolation, but ultimately for full control you would have to rebuild the effect using other means, which is perfectly doable, but a bit complex.

Mylenium

Hi, I think you should put the lightning on a new solid layer, not in the pink layer, that caused the pink layer disappeared...

Try to post some screenshots to show us what's wrong!! the one you post looks fine but we can't see the issue you have, so try to explain more about your issue, 

anyway when you apply the Advance lighting effect your solid will disappear, so you should apply the effects on a new solid layer.