These are endings of the reflexive verb. Reflexive verbs in Russian have a number of meanings, notably:
- 'myself': я мно́го трениру́юсь 'I train (myself) a lot' — я мно́го трениру́ю свою́ кома́нду 'I train my team a lot',
- 'each other': они́ руга́ются 'they argue (curse each other)' — они́ руга́ют поли́тика 'they severely criticise/curse the politician',
- passive meaning: кни́га хорошо́ продаётся 'the book is sold well',
- to show the action directed at a subject that is unimportant: соба́́ка куса́ется 'the dog bites' (it doesn't matter whom it bites exactly).
"I practice a lot" would usually be translated «я мно́го практику́юсь».
I'm pretty sure it's two syllables. Whenever you're uncertain about a pronounciation (as on Duolingo they're good, but far from perfect) I usually go to forvo.com which has a LOAD of pronounciations in pretty much any language you could hope for. Тренируюсь is also there, pronounced with ую as two syllables.