Are "arithmetic" and "rhythm" related?

Question

The online etymology dictionary says that arithmetic comes from Greek arithmos, from PIE *re(i)- "to reason, count" and gives as cognates English "read", Old High German "rim" "number", Old Irish rim "number," and Latin ritus "religious custom".

This etymology is suspicious. First, there were no roots starting wit r- in PIE. But this can be explained adding a laryngeal before it. What is more suspicious is that Latin ritus is known to come from the PIE root a̯er- "fit" and cognate to the words artist, army, aristocracy, Aryan, etc.

Also the same dictionary claims that English word row comes from PIE *rei- "to scratch, tear, cut". As to me, the meanings "to tear" and "to reason, count" seem totally different.

Regarding rhythm the dictionary says to come via Greek rhythmos from PIE *sreu- "to flow".

That said, I would like a clarification

1. Whether Greek rhythmos "arrangement, order, proportion" and arithmos "number" related.

2. Whether arithmos is related to artist, aristocracy etc.

3. Where to put English row and Russian ряд "r'ad" meaning "row" (Mallory and Adams put Lithuanian rinda "row" and Latvian rida "in rows" as related to arithmos and count the both related to ratio, artist etc).

4. Where to put the Italic *ord- "to arrange, arrangement" (> Eng. order), whether it is related to PIE a̯rtus "order, arrangement, juncture" (the dictionary claims it is of unknown origin)

Answer 1

ἀριθμός and ῥυθμός both have the suffix -θμο-, otherwise they are not related. The mainstream view, as reflected now in Beekes’s Greek etymological dictionary, is that ἀριθμός is from IE *h2rei- ‘to count’, whence also ON rim ‘account’, OHG rīm ‘row, number’, OIr. rim ‘number’, and ‘probably’, Lat. rītus ‘religious observance, rite’ < *h2rei-ti-.

ῥυθμός is from *sreu- “to stream”.

The origin of ἄριστος “best” (as in aristocracy etc.) is considered to be uncertain, but it cannot very well be connected to the aforementioned words, nor with Latin ars (as in artist).