yes,for example： 衣，一，医 all share the same pronunciation “yi” in the first tone。 ’一’also has 3 different pronunciations， ‘yi’ in first tone and the second tone and the fourth tone， in ‘一个’ it sounds in second tone，means one thing； in “一” which means number 1，then it sounds in first tone； in ‘一心一意’， which means concentrated on something， the first‘一’ sounds in the fourth tone， the second‘一’in the second tone. But basically, you don't need to care about the tones very much, every Chinese can understand you no matter which tone you use. many Chinese characters have different pronunciations completely different for example the Chinese character ‘藏’， in '西藏' which means tibet， it sounds like ‘zang’ in the fourth tone， but in ‘藏起来’which means hide， it sounds like ‘cang’ in the second tone， then you should be careful.

Everything you say is right. That's the difficult part of Chinese, and not only context determines what meaning has the syllable, sometimes it depends of what is attached to it. 天，Sky, 天师, Angel.

Chinese has experienced in the last millenium a shrinking in word lenght, and now 90% of chinese words are monosyllabic, so many words got to have the same pronounce. There is a whole poem based just one phoneme "shi".

Your pronunciation will improve as you keep on practicing, so don't worry about it so much and keep going.

医 is for doctor of medicine, medical science and 生 is for life, to give birth. I would recommend downloading the app called Pleco

Duolingo doesn't seem to teach chinese, this is just learning through trial and error

It's been happening all though the course, especially with the compound words like that

If you want to know the meaning of the word just press on the chines word

You dont need to say that it's more doctors, you can get it from context.

It's like am/is/are in English. 他的电话号码是 (Tā de diànhuà hàomǎ shì) : His phone number IS...