"Palatalization" means that a consonants is pronounced with the middle part of your tongue raised towards the roof of your mouth. This motion similar to what you do when pronouncing the "y" in "yes", only simultaneously with pronouncing the target consonant.
The exact realisation is better learnt by learning from audio samples in the language you are trying to learn. I think platalalized т and д in Russian are a bit different from those used in Ukrainian because we tend to mix in a little touch of an "s"-like sound into these. Ukrainians don't (at least, not in the standard language).
Seth, today is our lucky day. http://russianmentor.net/gram/mailbag/topics/phon1.htm
"Boy eats our apple" is an example of a particular type of telegraphic English, only used in particular cases like newspaper headlines. As one of the greatest problems encountered by Russian learners of English is correct use of articles, I do not think it would be a good idea for "Duo" to accept sentences like this.
I don't have a problem with playing with the rules. This isn't the place to start though. For a language learning course, they should require what is currently normal acceptable English.
Now if you want to start writing, you can use whatever grammar and vocabulary you like, and if your writing is good I won't complain once about either.
Language is the art of communicating. As with music, where beginners start with a predefined set of chords and harmonics established over centuries as "good form", authors frequently grow outside the constraints of the past. If we wish to ask whether something is good English, we have to ask whether it communicates well. If it does, then the grammar is irrelevant. Some writers "boldly go where no man has gone before". No apologies for the terrible grammar! :-) So.. coming back to "Boy eats apple. Boy is ill."...
It appears saying I have a typo in my answer, this is after i butchered the spelling about 5 times and have had to redo the same four questions over and over again in my practice, which was frustrating. http://imgur.com/a/8flub EDIT: Might be a missing "ь" that isn't showing up in the correction, or the "e" looks a bit different.