How to read these verses in the Quran?

Assalamu alaikum. I am learning how to read Arrabic alphabets and how to read Quran. I'm slightly confused with something: In the first verse of Sura Al-Faatiha, the spelling suggests the following reading > Bismi Allahi alrahmani alraheemi. But the actual reading that I heard from many recitations are like > Bismi-lla(h)i-lrahmani-raheem. So the 'al' was connected really fast, almost indistinguishable to my ear. And the 'i' in the end of 'alraheemi' was omitted. ____ My second example is the third verse of Al-Faatiha, which looks to me like > Maliki yawmi aldiyni But in the recitations it was like > Maliki yawmi-diyn So again 'al' was connected really fast and 'i' in the end was omitted. ____ Please help me understand the correct way to read the suras (I guess the word is tajweed), or point me toward some references. Thank you very much.