It would be hard to answer your questions without using a phonetical transcription (IPA, which is the most widespread, I believe) as well as some phonetical notions. I hope it is no problem.
When it stands by itself the numeral “dez” is stressed on its unique vowel: [ˈdɛʃ]. When it is combined with another numeral, the resulting compound word bears only one stress, on its second element, “seis” in the case of “dezasseis”, which means that the “dez” part is unstressed, and its vowel is weakened to [ə]; so, yes, “dez” is pronounced differently when it is alone and when it appears in a compound word such as “dezasseis”: [dəzəˈsejʃ] in a careful speech and [dzəˈsejʃ] in a swift speech.
In “dezoito”, as far as “dez” is concerned, it is the same as above. But there is something else, the final o, which is pronounced [u]. In Portuguese the vowel [u] can become voiceless (as if you were whispering) when it is unstressed and between two voiceless consonants (for instance the o in “costume”, habit) or between a voiceless consonant and nothing (that is to say in the end of a sentence). So “oito” is [ˈojtu], with a voiced or voiceless [u], which becomes [ˈojt] in a swift speech. If you listen carefully to the speaker, you will notice that sometimes she pronounces a final o as voiceless, and sometimes she does not pronounce it at all.
If you pronounce “dezoito” as “dez oito”, I suppose a Portuguese would understand “10, 8”, not “18”.
I hope it did not give you a headache