how to slow down tree decaying
I just found out that if you use hints a lot (moving your mouse over words so that the definition shows up) will make your tree decay faster, it will decay faster because when you use a hint Duolingo assumes that you don't know what the word means at all. Duolingo decides what your strength is for the skills by checking the strength of the words. If you use a hint Duolingo will pull the strength of the words down some, and your tree will decay faster. So only use a hint when you don't know a word at all!
People say that, although I've never seen an authoritative reference for it. Since it's not nice to be "penalized" for something you have no control over (i.e. not knowing a new-to-you word) and since it's an appealing notion at first glance, I think it's widely believed (and might even be true; I hardly have any inside information); however, viewed in another light, actually this wouldn't make much sense at all.
After all, what does it mean if you can get a sentence right without having to peek at a newly-introduced word? If you know (or are able to guess, let's presume for the moment based on some knowledge you have) a word before being "taught" it, it would be only sensible for your word strength for it to be quite high from the get-go. And it would make sense for the peeking to yield "typical" decay, whatever that may be.
That is true. This blog post also has some good advice on keeping your tree golden: http://gregreflects.blogspot.com/2014/12/how-to-make-gold-duolingo-tree.html?m=1
(And yes, I've posted this elsewhere, too, but it is a very informational and useful post.)
I agree that the Words tab provides a good resource for identifying words that need practice. However, it is not currently available in all the languages offered on Duolingo. For me, the Word tab appears in Spanish, French, and German, but is absent in Russian, Ukrainian and Catalán.
Ah, I just checked, the UI changes depending on what language you are currently working on at the time. Duolingo needs to get on fixing that, and put the "Words" tab up there for all the other languages. In the meantime, the best thing to do is to just do as many practices as you can, until you finish your specific language lesson and get your little gold trophy.