The shortest non-esoteric word with 5 consonants in a row is angsts. The longest such word that contains only one vowel used only once is strengths.
The longest such word that contains only one vowel that is used more than once is strengthlessnesses. Archchronicler, catchphrase, eschscholtzia, latchstring, lengthsman, and postphthisic each have six consonants in a row. BTW, Harrods London address is 87-135 Brompton Road, Knightsbridge.
Accepting y as a consonant - one might include
rhythm, syzygy and others.
Allowing vowel-less words, tsktsk, Hmmmmm et al
are welcome to the list and qualify as an answer to Q1.
The above is not an exhaustive list - multitude of samples are available and can be found on the web.
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